Solve (4x)^2+6^2=(5x)^2

$$( 4 x ) ^ { 2 } + 6 ^ { 2 } = ( 5 x ) ^ { 2 }$$

Solve for x

$$x=2$$

$$x=-2$$

Steps by Finding Square Root

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

$$4^{2}x^{2}+6^{2}=\left(5x\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}+6^{2}=\left(5x\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$16x^{2}+36=\left(5x\right)^{2}$$

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

$$16x^{2}+36=5^{2}x^{2}$$

Calculate 5 to the power of 2 and get 25.

$$16x^{2}+36=25x^{2}$$

Subtract 25x^{2} from both sides.

$$16x^{2}+36-25x^{2}=0$$

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

$$-9x^{2}+36=0$$

Subtract 36 from both sides. Anything subtracted from zero gives its negation.

$$-9x^{2}=-36$$

Divide both sides by -9.

$$x^{2}=\frac{-36}{-9}$$

Divide -36 by -9 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

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

$$4^{2}x^{2}+6^{2}=\left(5x\right)^{2}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}+6^{2}=\left(5x\right)^{2}$$

Calculate 6 to the power of 2 and get 36.

$$16x^{2}+36=\left(5x\right)^{2}$$

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

$$16x^{2}+36=5^{2}x^{2}$$

Calculate 5 to the power of 2 and get 25.

$$16x^{2}+36=25x^{2}$$

Subtract 25x^{2} from both sides.

$$16x^{2}+36-25x^{2}=0$$

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

$$-9x^{2}+36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -9 for a, 0 for b, and 36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-9\right)\times 36}}{2\left(-9\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-9\right)\times 36}}{2\left(-9\right)}$$

Multiply -4 times -9.

$$x=\frac{0±\sqrt{36\times 36}}{2\left(-9\right)}$$

Multiply 36 times 36.

$$x=\frac{0±\sqrt{1296}}{2\left(-9\right)}$$

Take the square root of 1296.

$$x=\frac{0±36}{2\left(-9\right)}$$

Multiply 2 times -9.

$$x=\frac{0±36}{-18}$$

Now solve the equation x=\frac{0±36}{-18} when ± is plus. Divide 36 by -18.

$$x=-2$$

Now solve the equation x=\frac{0±36}{-18} when ± is minus. Divide -36 by -18.

$$x=2$$

The equation is now solved.

$$x=-2 x=2$$