Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x=4-3(3x-8)
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Equation x/9+x=-10/3
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Equation √(x^2-1)=2*x
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Equation 4(x-3)=x+6
- Express {x} in terms of y where:
- -6*x-20*y=8
- -9*x-15*y=-4
- 1*x+5*y=-11
- 12*x-14*y=20
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Identical expressions
- x*(x- three)*x+ four *x- seven = zero
- x multiply by (x minus 3) multiply by x plus 4 multiply by x minus 7 equally 0
- x multiply by (x minus three) multiply by x plus four multiply by x minus seven equally zero
- x(x-3)x+4x-7=0
- xx-3x+4x-7=0
- x*(x-3)*x+4*x-7=O
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Similar expressions
- x*(x-3)*x-4*x-7=0
- x*(x+3)*x+4*x-7=0
- x*(x-3)*x+4*x+7=0
x*(x-3)*x+4*x-7=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
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x*(x - 3)*x + 4*x - 7 = 0
$$\left(x x \left(x - 3\right) + 4 x\right) - 7 = 0$$
Rapid solution
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______________ / ______________ \
/ ______ | / ______ |
/ 5 \/ 2037 | ___ / 5 \/ 2037 |
3 / - + -------- | \/ 3 *3 / - + -------- ___ |
\/ 2 18 1 | \/ 2 18 \/ 3 |
x1 = 1 - ------------------- + --------------------- + I*|- ------------------------- - ---------------------|
2 ______________ | 2 ______________|
/ ______ | / ______ |
/ 5 \/ 2037 | / 5 \/ 2037 |
6*3 / - + -------- | 6*3 / - + -------- |
\/ 2 18 \ \/ 2 18 /
$$x_{1} = - \frac{\sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} + \frac{1}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} - \frac{\sqrt{3}}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}\right)$$
______________ / ______________ \
/ ______ | / ______ |
/ 5 \/ 2037 | ___ / 5 \/ 2037 |
3 / - + -------- |\/ 3 *3 / - + -------- ___ |
\/ 2 18 1 | \/ 2 18 \/ 3 |
x2 = 1 - ------------------- + --------------------- + I*|------------------------- + ---------------------|
2 ______________ | 2 ______________|
/ ______ | / ______ |
/ 5 \/ 2037 | / 5 \/ 2037 |
6*3 / - + -------- | 6*3 / - + -------- |
\/ 2 18 \ \/ 2 18 /
$$x_{2} = - \frac{\sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} + \frac{1}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + i \left(\frac{\sqrt{3}}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2}\right)$$
______________
/ ______
/ 5 \/ 2037 1
x3 = 1 + 3 / - + -------- - ---------------------
\/ 2 18 ______________
/ ______
/ 5 \/ 2037
3*3 / - + --------
\/ 2 18
$$x_{3} = - \frac{1}{3 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}$$
x3 = -1/(3*(5/2 + sqrt(2037)/18)^(1/3)) + 1 + (5/2 + sqrt(2037)/18)^(1/3)
Sum and product of roots
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sum
______________ / ______________ \ ______________ / ______________ \
/ ______ | / ______ | / ______ | / ______ |
/ 5 \/ 2037 | ___ / 5 \/ 2037 | / 5 \/ 2037 | ___ / 5 \/ 2037 | ______________
3 / - + -------- | \/ 3 *3 / - + -------- ___ | 3 / - + -------- |\/ 3 *3 / - + -------- ___ | / ______
\/ 2 18 1 | \/ 2 18 \/ 3 | \/ 2 18 1 | \/ 2 18 \/ 3 | / 5 \/ 2037 1
1 - ------------------- + --------------------- + I*|- ------------------------- - ---------------------| + 1 - ------------------- + --------------------- + I*|------------------------- + ---------------------| + 1 + 3 / - + -------- - ---------------------
2 ______________ | 2 ______________| 2 ______________ | 2 ______________| \/ 2 18 ______________
/ ______ | / ______ | / ______ | / ______ | / ______
/ 5 \/ 2037 | / 5 \/ 2037 | / 5 \/ 2037 | / 5 \/ 2037 | / 5 \/ 2037
6*3 / - + -------- | 6*3 / - + -------- | 6*3 / - + -------- | 6*3 / - + -------- | 3*3 / - + --------
\/ 2 18 \ \/ 2 18 / \/ 2 18 \ \/ 2 18 / \/ 2 18
$$\left(- \frac{1}{3 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} + \frac{1}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} - \frac{\sqrt{3}}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} + \frac{1}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + i \left(\frac{\sqrt{3}}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2}\right)\right)\right)$$
=
/ ______________ \ / ______________ \
| / ______ | | / ______ |
| ___ / 5 \/ 2037 | | ___ / 5 \/ 2037 |
|\/ 3 *3 / - + -------- ___ | | \/ 3 *3 / - + -------- ___ |
| \/ 2 18 \/ 3 | | \/ 2 18 \/ 3 |
3 + I*|------------------------- + ---------------------| + I*|- ------------------------- - ---------------------|
| 2 ______________| | 2 ______________|
| / ______ | | / ______ |
| / 5 \/ 2037 | | / 5 \/ 2037 |
| 6*3 / - + -------- | | 6*3 / - + -------- |
\ \/ 2 18 / \ \/ 2 18 /
$$3 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} - \frac{\sqrt{3}}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}\right) + i \left(\frac{\sqrt{3}}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2}\right)$$
product
/ ______________ / ______________ \\ / ______________ / ______________ \\ | / ______ | / ______ || | / ______ | / ______ || | / 5 \/ 2037 | ___ / 5 \/ 2037 || | / 5 \/ 2037 | ___ / 5 \/ 2037 || / ______________ \ | 3 / - + -------- | \/ 3 *3 / - + -------- ___ || | 3 / - + -------- |\/ 3 *3 / - + -------- ___ || | / ______ | | \/ 2 18 1 | \/ 2 18 \/ 3 || | \/ 2 18 1 | \/ 2 18 \/ 3 || | / 5 \/ 2037 1 | |1 - ------------------- + --------------------- + I*|- ------------------------- - ---------------------||*|1 - ------------------- + --------------------- + I*|------------------------- + ---------------------||*|1 + 3 / - + -------- - ---------------------| | 2 ______________ | 2 ______________|| | 2 ______________ | 2 ______________|| | \/ 2 18 ______________| | / ______ | / ______ || | / ______ | / ______ || | / ______ | | / 5 \/ 2037 | / 5 \/ 2037 || | / 5 \/ 2037 | / 5 \/ 2037 || | / 5 \/ 2037 | | 6*3 / - + -------- | 6*3 / - + -------- || | 6*3 / - + -------- | 6*3 / - + -------- || | 3*3 / - + -------- | \ \/ 2 18 \ \/ 2 18 // \ \/ 2 18 \ \/ 2 18 // \ \/ 2 18 /
$$\left(- \frac{\sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} + \frac{1}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + i \left(\frac{\sqrt{3}}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + \frac{\sqrt{3} \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} + \frac{1}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}{2} - \frac{\sqrt{3}}{6 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}}\right)\right) \left(- \frac{1}{3 \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}} + 1 + \sqrt[3]{\frac{5}{2} + \frac{\sqrt{2037}}{18}}\right)$$
=
___________________ 2/3 __________________ ___________________ 2/3 __________________ 2/3 2/3
3 / ______ 3 ___ / ______\ 2/3 3 / ______ ______ 3 / ______ 3 ____ / ______\ 2/3 ______ 3 / ______ 3 ___ ______ / ______\ 3 ___ 6 ___ _____ / ______\
15*\/ 540 + 12*\/ 2037 225*\/ 2 *\135 + 3*\/ 2037 / 15*2 *\/ 135 + 3*\/ 2037 \/ 2037 *\/ 540 + 12*\/ 2037 225*\/ 18 *\45 + \/ 2037 / 2 *\/ 2037 *\/ 135 + 3*\/ 2037 5*\/ 2 *\/ 2037 *\135 + 3*\/ 2037 / 15*\/ 2 *\/ 3 *\/ 679 *\45 + \/ 2037 /
7 + ------------------------- - ------------------------------- - ----------------------------- - ------------------------------- + ----------------------------- + ----------------------------------- + -------------------------------------- - -----------------------------------------
16 32 16 48 32 48 32 32
$$- \frac{15 \sqrt[3]{2} \sqrt[6]{3} \sqrt{679} \left(45 + \sqrt{2037}\right)^{\frac{2}{3}}}{32} - \frac{225 \sqrt[3]{2} \left(135 + 3 \sqrt{2037}\right)^{\frac{2}{3}}}{32} - \frac{\sqrt{2037} \sqrt[3]{540 + 12 \sqrt{2037}}}{48} - \frac{15 \cdot 2^{\frac{2}{3}} \sqrt[3]{135 + 3 \sqrt{2037}}}{16} + 7 + \frac{15 \sqrt[3]{540 + 12 \sqrt{2037}}}{16} + \frac{2^{\frac{2}{3}} \sqrt{2037} \sqrt[3]{135 + 3 \sqrt{2037}}}{48} + \frac{225 \sqrt[3]{18} \left(45 + \sqrt{2037}\right)^{\frac{2}{3}}}{32} + \frac{5 \sqrt[3]{2} \sqrt{2037} \left(135 + 3 \sqrt{2037}\right)^{\frac{2}{3}}}{32}$$
7 + 15*(540 + 12*sqrt(2037))^(1/3)/16 - 225*2^(1/3)*(135 + 3*sqrt(2037))^(2/3)/32 - 15*2^(2/3)*(135 + 3*sqrt(2037))^(1/3)/16 - sqrt(2037)*(540 + 12*sqrt(2037))^(1/3)/48 + 225*18^(1/3)*(45 + sqrt(2037))^(2/3)/32 + 2^(2/3)*sqrt(2037)*(135 + 3*sqrt(2037))^(1/3)/48 + 5*2^(1/3)*sqrt(2037)*(135 + 3*sqrt(2037))^(2/3)/32 - 15*2^(1/3)*3^(1/6)*sqrt(679)*(45 + sqrt(2037))^(2/3)/32
Numerical answer
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x1 = 2.51598022769282
x2 = 0.24200988615359 - 1.65034755068945*i
x3 = 0.24200988615359 + 1.65034755068945*i
x3 = 0.24200988615359 + 1.65034755068945*i