Solve x^2=(5/4x)^2+9^2

$$x ^ { 2 } = ( 5 / 4 x ) ^ { 2 } + 9 ^ { 2 }$$

Solve for x (complex solution)

$$x=12i$$

$$x=-12i$$

Steps by Finding Square Root

Expand \left(\frac{5}{4}x\right)^{2}.

$$x^{2}=\left(\frac{5}{4}\right)^{2}x^{2}+9^{2}$$

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$x^{2}=\frac{25}{16}x^{2}+9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}=\frac{25}{16}x^{2}+81$$

Subtract \frac{25}{16}x^{2} from both sides.

$$x^{2}-\frac{25}{16}x^{2}=81$$

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

$$-\frac{9}{16}x^{2}=81$$

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

$$x^{2}=81\left(-\frac{16}{9}\right)$$

Multiply 81 and -\frac{16}{9} to get -144.

$$x^{2}=-144$$

The equation is now solved.

$$x=12i x=-12i$$

Steps Using the Quadratic Formula

Expand \left(\frac{5}{4}x\right)^{2}.

$$x^{2}=\left(\frac{5}{4}\right)^{2}x^{2}+9^{2}$$

Calculate \frac{5}{4} to the power of 2 and get \frac{25}{16}.

$$x^{2}=\frac{25}{16}x^{2}+9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}=\frac{25}{16}x^{2}+81$$

Subtract \frac{25}{16}x^{2} from both sides.

$$x^{2}-\frac{25}{16}x^{2}=81$$

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

$$-\frac{9}{16}x^{2}=81$$

Subtract 81 from both sides.

$$-\frac{9}{16}x^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{9}{16} for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{9}{16}\right)\left(-81\right)}}{2\left(-\frac{9}{16}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{9}{16}\right)\left(-81\right)}}{2\left(-\frac{9}{16}\right)}$$

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

$$x=\frac{0±\sqrt{\frac{9}{4}\left(-81\right)}}{2\left(-\frac{9}{16}\right)}$$

Multiply \frac{9}{4} times -81.

$$x=\frac{0±\sqrt{-\frac{729}{4}}}{2\left(-\frac{9}{16}\right)}$$

Take the square root of -\frac{729}{4}.

$$x=\frac{0±\frac{27}{2}i}{2\left(-\frac{9}{16}\right)}$$

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

$$x=\frac{0±\frac{27}{2}i}{-\frac{9}{8}}$$

Now solve the equation x=\frac{0±\frac{27}{2}i}{-\frac{9}{8}} when ± is plus.

$$x=-12i$$

Now solve the equation x=\frac{0±\frac{27}{2}i}{-\frac{9}{8}} when ± is minus.

$$x=12i$$

The equation is now solved.

$$x=-12i x=12i$$