Solve x^2+32^2={left(5/3xright)}^2

$${ x }^{ 2 } + { 32 }^{ 2 } = { \left( \frac{ 5 }{ 3 } x \right) }^{ 2 }$$

Solve for x

$$x=24$$

$$x=-24$$

Steps by Finding Square Root

Calculate 32 to the power of 2 and get 1024.

$$x^{2}+1024=\left(\frac{5}{3}x\right)^{2}$$

Expand \left(\frac{5}{3}x\right)^{2}.

$$x^{2}+1024=\left(\frac{5}{3}\right)^{2}x^{2}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$x^{2}+1024=\frac{25}{9}x^{2}$$

Subtract \frac{25}{9}x^{2} from both sides.

$$x^{2}+1024-\frac{25}{9}x^{2}=0$$

Combine x^{2} and -\frac{25}{9}x^{2} to get -\frac{16}{9}x^{2}.

$$-\frac{16}{9}x^{2}+1024=0$$

Subtract 1024 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{16}{9}x^{2}=-1024$$

Multiply both sides by -\frac{9}{16}, the reciprocal of -\frac{16}{9}.

$$x^{2}=-1024\left(-\frac{9}{16}\right)$$

Multiply -1024 and -\frac{9}{16} to get 576.

$$x^{2}=576$$

Take the square root of both sides of the equation.

$$x=24 x=-24$$

Steps Using the Quadratic Formula

Calculate 32 to the power of 2 and get 1024.

$$x^{2}+1024=\left(\frac{5}{3}x\right)^{2}$$

Expand \left(\frac{5}{3}x\right)^{2}.

$$x^{2}+1024=\left(\frac{5}{3}\right)^{2}x^{2}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$x^{2}+1024=\frac{25}{9}x^{2}$$

Subtract \frac{25}{9}x^{2} from both sides.

$$x^{2}+1024-\frac{25}{9}x^{2}=0$$

Combine x^{2} and -\frac{25}{9}x^{2} to get -\frac{16}{9}x^{2}.

$$-\frac{16}{9}x^{2}+1024=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{16}{9} for a, 0 for b, and 1024 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{16}{9}\right)\times 1024}}{2\left(-\frac{16}{9}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{16}{9}\right)\times 1024}}{2\left(-\frac{16}{9}\right)}$$

Multiply -4 times -\frac{16}{9}.

$$x=\frac{0±\sqrt{\frac{64}{9}\times 1024}}{2\left(-\frac{16}{9}\right)}$$

Multiply \frac{64}{9} times 1024.

$$x=\frac{0±\sqrt{\frac{65536}{9}}}{2\left(-\frac{16}{9}\right)}$$

Take the square root of \frac{65536}{9}.

$$x=\frac{0±\frac{256}{3}}{2\left(-\frac{16}{9}\right)}$$

Multiply 2 times -\frac{16}{9}.

$$x=\frac{0±\frac{256}{3}}{-\frac{32}{9}}$$

Now solve the equation x=\frac{0±\frac{256}{3}}{-\frac{32}{9}} when ± is plus.

$$x=-24$$

Now solve the equation x=\frac{0±\frac{256}{3}}{-\frac{32}{9}} when ± is minus.

$$x=24$$

The equation is now solved.

$$x=-24 x=24$$