Solve x^2-25=left(9xright)^2-784

$${ x }^{ 2 } -25= { \left(9x \right) }^{ 2 } -784$$

Solve for x

$$x = \frac{\sqrt{3795}}{20} \approx 3.080178566$$

$$x = -\frac{\sqrt{3795}}{20} \approx -3.080178566$$

Steps by Finding Square Root

Expand \left(9x\right)^{2}.

$$x^{2}-25=9^{2}x^{2}-784$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}-25=81x^{2}-784$$

Subtract 81x^{2} from both sides.

$$x^{2}-25-81x^{2}=-784$$

Combine x^{2} and -81x^{2} to get -80x^{2}.

$$-80x^{2}-25=-784$$

Add 25 to both sides.

$$-80x^{2}=-784+25$$

Add -784 and 25 to get -759.

$$-80x^{2}=-759$$

Divide both sides by -80.

$$x^{2}=\frac{-759}{-80}$$

Fraction \frac{-759}{-80} can be simplified to \frac{759}{80} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{759}{80}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3795}}{20} x=-\frac{\sqrt{3795}}{20}$$

Steps Using the Quadratic Formula

Expand \left(9x\right)^{2}.

$$x^{2}-25=9^{2}x^{2}-784$$

Calculate 9 to the power of 2 and get 81.

$$x^{2}-25=81x^{2}-784$$

Subtract 81x^{2} from both sides.

$$x^{2}-25-81x^{2}=-784$$

Combine x^{2} and -81x^{2} to get -80x^{2}.

$$-80x^{2}-25=-784$$

Add 784 to both sides.

$$-80x^{2}-25+784=0$$

Add -25 and 784 to get 759.

$$-80x^{2}+759=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -80 for a, 0 for b, and 759 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-80\right)\times 759}}{2\left(-80\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-80\right)\times 759}}{2\left(-80\right)}$$

Multiply -4 times -80.

$$x=\frac{0±\sqrt{320\times 759}}{2\left(-80\right)}$$

Multiply 320 times 759.

$$x=\frac{0±\sqrt{242880}}{2\left(-80\right)}$$

Take the square root of 242880.

$$x=\frac{0±8\sqrt{3795}}{2\left(-80\right)}$$

Multiply 2 times -80.

$$x=\frac{0±8\sqrt{3795}}{-160}$$

Now solve the equation x=\frac{0±8\sqrt{3795}}{-160} when ± is plus.

$$x=-\frac{\sqrt{3795}}{20}$$

Now solve the equation x=\frac{0±8\sqrt{3795}}{-160} when ± is minus.

$$x=\frac{\sqrt{3795}}{20}$$

The equation is now solved.

$$x=-\frac{\sqrt{3795}}{20} x=\frac{\sqrt{3795}}{20}$$