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Equation 6x-3x+1=8
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- Express {x} in terms of y where:
- -6*x+12*y=11
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- Expression:
- 480
-
Identical expressions
- twenty-four /sqrt(one +(x/(fifty thousand / twenty-four))^ two)* twenty-four /sqrt(one +(x/(fifty thousand / twenty-four))^ two)= four hundred and eighty
- 24 divide by square root of (1 plus (x divide by (50000 divide by 24)) squared ) multiply by 24 divide by square root of (1 plus (x divide by (50000 divide by 24)) squared ) equally 480
- twenty minus four divide by square root of (one plus (x divide by (fifty thousand divide by twenty minus four)) to the power of two) multiply by twenty minus four divide by square root of (one plus (x divide by (fifty thousand divide by twenty minus four)) to the power of two) equally four hundred and eighty
- 24/√(1+(x/(50000/24))^2)*24/√(1+(x/(50000/24))^2)=480
- 24/sqrt(1+(x/(50000/24))2)*24/sqrt(1+(x/(50000/24))2)=480
- 24/sqrt1+x/50000/242*24/sqrt1+x/50000/242=480
- 24/sqrt(1+(x/(50000/24))²)*24/sqrt(1+(x/(50000/24))²)=480
- 24/sqrt(1+(x/(50000/24)) to the power of 2)*24/sqrt(1+(x/(50000/24)) to the power of 2)=480
- 24/sqrt(1+(x/(50000/24))^2)24/sqrt(1+(x/(50000/24))^2)=480
- 24/sqrt(1+(x/(50000/24))2)24/sqrt(1+(x/(50000/24))2)=480
- 24/sqrt1+x/50000/24224/sqrt1+x/50000/242=480
- 24/sqrt1+x/50000/24^224/sqrt1+x/50000/24^2=480
- 24 divide by sqrt(1+(x divide by (50000 divide by 24))^2)*24 divide by sqrt(1+(x divide by (50000 divide by 24))^2)=480
-
Similar expressions
- 24/sqrt(1-(x/(50000/24))^2)*24/sqrt(1+(x/(50000/24))^2)=480
- 24/sqrt(1+(x/(50000/24))^2)*24/sqrt(1-(x/(50000/24))^2)=480
24/sqrt(1+(x/(50000/24))^2)*24/sqrt(1+(x/(50000/24))^2)=480 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
24
--------------------*24
_______________
/ 2
/ / x \
/ 1 + |------|
\/ \6250/3/
----------------------- = 480
_______________
/ 2
/ / x \
/ 1 + |------|
\/ \6250/3/
$$\frac{24 \frac{24}{\sqrt{\left(\frac{x}{\frac{6250}{3}}\right)^{2} + 1}}}{\sqrt{\left(\frac{x}{\frac{6250}{3}}\right)^{2} + 1}} = 480$$
Detail solution
Given the equation:
$$\frac{24 \frac{24}{\sqrt{\left(\frac{x}{\frac{6250}{3}}\right)^{2} + 1}}}{\sqrt{\left(\frac{x}{\frac{6250}{3}}\right)^{2} + 1}} = 480$$
Multiply the equation sides by the denominators:
1 + 9*x^2/39062500
we get:
$$\frac{576 \left(\frac{9 x^{2}}{39062500} + 1\right)}{\left(\frac{x}{\frac{6250}{3}}\right)^{2} + 1} = \frac{216 x^{2}}{1953125} + 480$$
$$576 = \frac{216 x^{2}}{1953125} + 480$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$576 = \frac{216 x^{2}}{1953125} + 480$$
to
$$96 - \frac{216 x^{2}}{1953125} = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = - \frac{216}{1953125}$$
$$b = 0$$
$$c = 96$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{1250 \sqrt{5}}{3}$$
$$x_{2} = \frac{1250 \sqrt{5}}{3}$$
$$\frac{24 \frac{24}{\sqrt{\left(\frac{x}{\frac{6250}{3}}\right)^{2} + 1}}}{\sqrt{\left(\frac{x}{\frac{6250}{3}}\right)^{2} + 1}} = 480$$
Multiply the equation sides by the denominators:
1 + 9*x^2/39062500
we get:
$$\frac{576 \left(\frac{9 x^{2}}{39062500} + 1\right)}{\left(\frac{x}{\frac{6250}{3}}\right)^{2} + 1} = \frac{216 x^{2}}{1953125} + 480$$
$$576 = \frac{216 x^{2}}{1953125} + 480$$
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$576 = \frac{216 x^{2}}{1953125} + 480$$
to
$$96 - \frac{216 x^{2}}{1953125} = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = - \frac{216}{1953125}$$
$$b = 0$$
$$c = 96$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-216/1953125) * (96) = 82944/1953125
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{1250 \sqrt{5}}{3}$$
$$x_{2} = \frac{1250 \sqrt{5}}{3}$$
Sum and product of roots
[src]
sum
___ ___
1250*\/ 5 1250*\/ 5
- ---------- + ----------
3 3
$$- \frac{1250 \sqrt{5}}{3} + \frac{1250 \sqrt{5}}{3}$$
=
0
$$0$$
product
___ ___
-1250*\/ 5 1250*\/ 5
-----------*----------
3 3
$$- \frac{1250 \sqrt{5}}{3} \frac{1250 \sqrt{5}}{3}$$
=
-7812500/9
$$- \frac{7812500}{9}$$
-7812500/9
Rapid solution
[src]
___
-1250*\/ 5
x1 = -----------
3
$$x_{1} = - \frac{1250 \sqrt{5}}{3}$$
___
1250*\/ 5
x2 = ----------
3
$$x_{2} = \frac{1250 \sqrt{5}}{3}$$
x2 = 1250*sqrt(5)/3