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- Equation:
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Equation x^2+2x+1=0
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Equation cos(x/2)=1/2
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Equation sin(x)=1,5
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Equation e^x=4
- Express {x} in terms of y where:
- 2*x+16*y=11
- -8*x+10*y=19
- -5*x+3*y=10
- 14*x-19*y=-6
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Identical expressions
- one hundred and ninety-two *sqrt(x)- twelve /(sqrt(x))+ twelve *x= three hundred and one
- 192 multiply by square root of (x) minus 12 divide by ( square root of (x)) plus 12 multiply by x equally 301
- one hundred and ninety minus two multiply by square root of (x) minus twelve divide by ( square root of (x)) plus twelve multiply by x equally three hundred and one
- 192*√(x)-12/(√(x))+12*x=301
- 192sqrt(x)-12/(sqrt(x))+12x=301
- 192sqrtx-12/sqrtx+12x=301
- 192*sqrt(x)-12 divide by (sqrt(x))+12*x=301
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Similar expressions
- 17/6:(x+217/30)*13/7=4=5/7
- 192*sqrt(x)+12/(sqrt(x))+12*x=301
- 192*sqrt(x)-12/(sqrt(x))-12*x=301
192*sqrt(x)-12/(sqrt(x))+12*x=301 equation
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The solution
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[src]
___ 12
192*\/ x - ----- + 12*x = 301
___
\/ x
$$12 x + \left(192 \sqrt{x} - \frac{12}{\sqrt{x}}\right) = 301$$
Rapid solution
[src]
/ 1 \ / / 1 \ \
13212649*re|---------------------------------------------------------| |13212649*im|---------------------------------------------------------| / / ___________\\ / / ___________\\| / / ___________\\ / / ___________\\
| ____________________________________| | | ____________________________________| | |86472*\/ 107039461 || | |86472*\/ 107039461 ||| | |86472*\/ 107039461 || | |86472*\/ 107039461 ||
|/ ___\ / ___________ | | |/ ___\ / ___________ | |atan|-------------------|| |atan|-------------------||| |atan|-------------------|| |atan|-------------------||
|| 1 I*\/ 3 | / 48018598955 1201*I*\/ 107039461 | | || 1 I*\/ 3 | / 48018598955 1201*I*\/ 107039461 | __________ | \ 48018598955 /| __________ | \ 48018598955 /|| __________ | \ 48018598955 /| __________ | \ 48018598955 /|
||- - - -------|*3 / ----------- + -------------------- | | ||- - - -------|*3 / ----------- + -------------------- | \/ 13212649 *sin|-------------------------| \/ 39637947 *cos|-------------------------|| \/ 13212649 *cos|-------------------------| \/ 39637947 *sin|-------------------------|
1837 \\ 2 2 / \/ 46656 648 / | \\ 2 2 / \/ 46656 648 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = ---- + ---------------------------------------------------------------------- + I*|---------------------------------------------------------------------- - ------------------------------------------- - -------------------------------------------| - ------------------------------------------- + -------------------------------------------
18 1296 \ 1296 72 72 / 72 72
$$x_{1} = - \frac{\sqrt{13212649} \cos{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{13212649 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{48018598955}{46656} + \frac{1201 \sqrt{107039461} i}{648}}}\right)}}{1296} + \frac{\sqrt{39637947} \sin{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{1837}{18} + i \left(- \frac{\sqrt{39637947} \cos{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} - \frac{\sqrt{13212649} \sin{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{13212649 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{48018598955}{46656} + \frac{1201 \sqrt{107039461} i}{648}}}\right)}}{1296}\right)$$
x1 = -sqrt(13212649)*cos(atan(86472*sqrt(107039461)/48018598955)/3)/72 + 13212649*re(1/((-1/2 - sqrt(3)*i/2)*(48018598955/46656 + 1201*sqrt(107039461)*i/648)^(1/3)))/1296 + sqrt(39637947)*sin(atan(86472*sqrt(107039461)/48018598955)/3)/72 + 1837/18 + i*(-sqrt(39637947)*cos(atan(86472*sqrt(107039461)/48018598955)/3)/72 - sqrt(13212649)*sin(atan(86472*sqrt(107039461)/48018598955)/3)/72 + 13212649*im(1/((-1/2 - sqrt(3)*i/2)*(48018598955/46656 + 1201*sqrt(107039461)*i/648)^(1/3)))/1296)
Sum and product of roots
[src]
sum
/ 1 \ / / 1 \ \
13212649*re|---------------------------------------------------------| |13212649*im|---------------------------------------------------------| / / ___________\\ / / ___________\\| / / ___________\\ / / ___________\\
| ____________________________________| | | ____________________________________| | |86472*\/ 107039461 || | |86472*\/ 107039461 ||| | |86472*\/ 107039461 || | |86472*\/ 107039461 ||
|/ ___\ / ___________ | | |/ ___\ / ___________ | |atan|-------------------|| |atan|-------------------||| |atan|-------------------|| |atan|-------------------||
|| 1 I*\/ 3 | / 48018598955 1201*I*\/ 107039461 | | || 1 I*\/ 3 | / 48018598955 1201*I*\/ 107039461 | __________ | \ 48018598955 /| __________ | \ 48018598955 /|| __________ | \ 48018598955 /| __________ | \ 48018598955 /|
||- - - -------|*3 / ----------- + -------------------- | | ||- - - -------|*3 / ----------- + -------------------- | \/ 13212649 *sin|-------------------------| \/ 39637947 *cos|-------------------------|| \/ 13212649 *cos|-------------------------| \/ 39637947 *sin|-------------------------|
1837 \\ 2 2 / \/ 46656 648 / | \\ 2 2 / \/ 46656 648 / \ 3 / \ 3 /| \ 3 / \ 3 /
---- + ---------------------------------------------------------------------- + I*|---------------------------------------------------------------------- - ------------------------------------------- - -------------------------------------------| - ------------------------------------------- + -------------------------------------------
18 1296 \ 1296 72 72 / 72 72
$$- \frac{\sqrt{13212649} \cos{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{13212649 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{48018598955}{46656} + \frac{1201 \sqrt{107039461} i}{648}}}\right)}}{1296} + \frac{\sqrt{39637947} \sin{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{1837}{18} + i \left(- \frac{\sqrt{39637947} \cos{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} - \frac{\sqrt{13212649} \sin{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{13212649 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{48018598955}{46656} + \frac{1201 \sqrt{107039461} i}{648}}}\right)}}{1296}\right)$$
=
/ 1 \ / / 1 \ \
13212649*re|---------------------------------------------------------| |13212649*im|---------------------------------------------------------| / / ___________\\ / / ___________\\| / / ___________\\ / / ___________\\
| ____________________________________| | | ____________________________________| | |86472*\/ 107039461 || | |86472*\/ 107039461 ||| | |86472*\/ 107039461 || | |86472*\/ 107039461 ||
|/ ___\ / ___________ | | |/ ___\ / ___________ | |atan|-------------------|| |atan|-------------------||| |atan|-------------------|| |atan|-------------------||
|| 1 I*\/ 3 | / 48018598955 1201*I*\/ 107039461 | | || 1 I*\/ 3 | / 48018598955 1201*I*\/ 107039461 | __________ | \ 48018598955 /| __________ | \ 48018598955 /|| __________ | \ 48018598955 /| __________ | \ 48018598955 /|
||- - - -------|*3 / ----------- + -------------------- | | ||- - - -------|*3 / ----------- + -------------------- | \/ 13212649 *sin|-------------------------| \/ 39637947 *cos|-------------------------|| \/ 13212649 *cos|-------------------------| \/ 39637947 *sin|-------------------------|
1837 \\ 2 2 / \/ 46656 648 / | \\ 2 2 / \/ 46656 648 / \ 3 / \ 3 /| \ 3 / \ 3 /
---- + ---------------------------------------------------------------------- + I*|---------------------------------------------------------------------- - ------------------------------------------- - -------------------------------------------| - ------------------------------------------- + -------------------------------------------
18 1296 \ 1296 72 72 / 72 72
$$- \frac{\sqrt{13212649} \cos{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{13212649 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{48018598955}{46656} + \frac{1201 \sqrt{107039461} i}{648}}}\right)}}{1296} + \frac{\sqrt{39637947} \sin{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{1837}{18} + i \left(- \frac{\sqrt{39637947} \cos{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} - \frac{\sqrt{13212649} \sin{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{13212649 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{48018598955}{46656} + \frac{1201 \sqrt{107039461} i}{648}}}\right)}}{1296}\right)$$
product
/ 1 \ / / 1 \ \
13212649*re|---------------------------------------------------------| |13212649*im|---------------------------------------------------------| / / ___________\\ / / ___________\\| / / ___________\\ / / ___________\\
| ____________________________________| | | ____________________________________| | |86472*\/ 107039461 || | |86472*\/ 107039461 ||| | |86472*\/ 107039461 || | |86472*\/ 107039461 ||
|/ ___\ / ___________ | | |/ ___\ / ___________ | |atan|-------------------|| |atan|-------------------||| |atan|-------------------|| |atan|-------------------||
|| 1 I*\/ 3 | / 48018598955 1201*I*\/ 107039461 | | || 1 I*\/ 3 | / 48018598955 1201*I*\/ 107039461 | __________ | \ 48018598955 /| __________ | \ 48018598955 /|| __________ | \ 48018598955 /| __________ | \ 48018598955 /|
||- - - -------|*3 / ----------- + -------------------- | | ||- - - -------|*3 / ----------- + -------------------- | \/ 13212649 *sin|-------------------------| \/ 39637947 *cos|-------------------------|| \/ 13212649 *cos|-------------------------| \/ 39637947 *sin|-------------------------|
1837 \\ 2 2 / \/ 46656 648 / | \\ 2 2 / \/ 46656 648 / \ 3 / \ 3 /| \ 3 / \ 3 /
---- + ---------------------------------------------------------------------- + I*|---------------------------------------------------------------------- - ------------------------------------------- - -------------------------------------------| - ------------------------------------------- + -------------------------------------------
18 1296 \ 1296 72 72 / 72 72
$$- \frac{\sqrt{13212649} \cos{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{13212649 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{48018598955}{46656} + \frac{1201 \sqrt{107039461} i}{648}}}\right)}}{1296} + \frac{\sqrt{39637947} \sin{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{1837}{18} + i \left(- \frac{\sqrt{39637947} \cos{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} - \frac{\sqrt{13212649} \sin{\left(\frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} \right)}}{72} + \frac{13212649 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{48018598955}{46656} + \frac{1201 \sqrt{107039461} i}{648}}}\right)}}{1296}\right)$$
=
/ / ___________\ \
| |86472*\/ 107039461 | |
| atan|-------------------| |
__________ | \ 48018598955 / pi|
\/ 13212649 *sin|- ------------------------- + --|
1837 \ 3 6 /
---- - --------------------------------------------------
18 18
$$- \frac{\sqrt{13212649} \sin{\left(- \frac{\operatorname{atan}{\left(\frac{86472 \sqrt{107039461}}{48018598955} \right)}}{3} + \frac{\pi}{6} \right)}}{18} + \frac{1837}{18}$$
1837/18 - sqrt(13212649)*sin(-atan(86472*sqrt(107039461)/48018598955)/3 + pi/6)/18