Solve (4x)^2=576

$$( 4 x ) ^ { 2 } = 576$$

Solve for x

$$x=6$$

$$x=-6$$

Steps Using Difference of Squares

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

$$4^{2}x^{2}=576$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}=576$$

Subtract 576 from both sides.

$$16x^{2}-576=0$$

Divide both sides by 16.

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

Consider x^{2}-36. Rewrite x^{2}-36 as x^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-6\right)\left(x+6\right)=0$$

To find equation solutions, solve x-6=0 and x+6=0.

$$x=6 x=-6$$

Steps by Finding Square Root

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

$$4^{2}x^{2}=576$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}=576$$

Divide both sides by 16.

$$x^{2}=\frac{576}{16}$$

Divide 576 by 16 to get 36.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

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

$$4^{2}x^{2}=576$$

Calculate 4 to the power of 2 and get 16.

$$16x^{2}=576$$

Subtract 576 from both sides.

$$16x^{2}-576=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 16 for a, 0 for b, and -576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 16\left(-576\right)}}{2\times 16}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 16\left(-576\right)}}{2\times 16}$$

Multiply -4 times 16.

$$x=\frac{0±\sqrt{-64\left(-576\right)}}{2\times 16}$$

Multiply -64 times -576.

$$x=\frac{0±\sqrt{36864}}{2\times 16}$$

Take the square root of 36864.

$$x=\frac{0±192}{2\times 16}$$

Multiply 2 times 16.

$$x=\frac{0±192}{32}$$

Now solve the equation x=\frac{0±192}{32} when ± is plus. Divide 192 by 32.

$$x=6$$

Now solve the equation x=\frac{0±192}{32} when ± is minus. Divide -192 by 32.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$