Solve 4(x-12)(x+12)=1

$$4 ( x - 12 ) ( x + 12 ) = 1$$

Solve for x

$$x = \frac{\sqrt{577}}{2} \approx 12.010412149$$

$$x = -\frac{\sqrt{577}}{2} \approx -12.010412149$$

Steps by Finding Square Root

Use the distributive property to multiply 4 by x-12.

$$\left(4x-48\right)\left(x+12\right)=1$$

Use the distributive property to multiply 4x-48 by x+12 and combine like terms.

$$4x^{2}-576=1$$

Add 576 to both sides.

$$4x^{2}=1+576$$

Add 1 and 576 to get 577.

$$4x^{2}=577$$

Divide both sides by 4.

$$x^{2}=\frac{577}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{577}}{2} x=-\frac{\sqrt{577}}{2}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 4 by x-12.

$$\left(4x-48\right)\left(x+12\right)=1$$

Use the distributive property to multiply 4x-48 by x+12 and combine like terms.

$$4x^{2}-576=1$$

Subtract 1 from both sides.

$$4x^{2}-576-1=0$$

Subtract 1 from -576 to get -577.

$$4x^{2}-577=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -577 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-577\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-577\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-577\right)}}{2\times 4}$$

Multiply -16 times -577.

$$x=\frac{0±\sqrt{9232}}{2\times 4}$$

Take the square root of 9232.

$$x=\frac{0±4\sqrt{577}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{577}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{577}}{8} when ± is plus.

$$x=\frac{\sqrt{577}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{577}}{8} when ± is minus.

$$x=-\frac{\sqrt{577}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{577}}{2} x=-\frac{\sqrt{577}}{2}$$