Solve 1/4(x+2)(x-2)-1=0

$$\frac { 1 } { 4 } ( x + 2 ) ( x - 2 ) - 1 = 0$$

Solve for x

$$x=2\sqrt{2}\approx 2.828427125$$

$$x=-2\sqrt{2}\approx -2.828427125$$

Steps by Finding Square Root

Use the distributive property to multiply \frac{1}{4} by x+2.

$$\left(\frac{1}{4}x+\frac{1}{2}\right)\left(x-2\right)-1=0$$

Use the distributive property to multiply \frac{1}{4}x+\frac{1}{2} by x-2 and combine like terms.

$$\frac{1}{4}x^{2}-1-1=0$$

Subtract 1 from -1 to get -2.

$$\frac{1}{4}x^{2}-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$\frac{1}{4}x^{2}=2$$

Multiply both sides by 4, the reciprocal of \frac{1}{4}.

$$x^{2}=2\times 4$$

Multiply 2 and 4 to get 8.

$$x^{2}=8$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Use the distributive property to multiply \frac{1}{4} by x+2.

$$\left(\frac{1}{4}x+\frac{1}{2}\right)\left(x-2\right)-1=0$$

Use the distributive property to multiply \frac{1}{4}x+\frac{1}{2} by x-2 and combine like terms.

$$\frac{1}{4}x^{2}-1-1=0$$

Subtract 1 from -1 to get -2.

$$\frac{1}{4}x^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1}{4} for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1}{4}\left(-2\right)}}{2\times \frac{1}{4}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1}{4}\left(-2\right)}}{2\times \frac{1}{4}}$$

Multiply -4 times \frac{1}{4}.

$$x=\frac{0±\sqrt{-\left(-2\right)}}{2\times \frac{1}{4}}$$

Multiply -1 times -2.

$$x=\frac{0±\sqrt{2}}{2\times \frac{1}{4}}$$

Multiply 2 times \frac{1}{4}.

$$x=\frac{0±\sqrt{2}}{\frac{1}{2}}$$

Now solve the equation x=\frac{0±\sqrt{2}}{\frac{1}{2}} when ± is plus.

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

Now solve the equation x=\frac{0±\sqrt{2}}{\frac{1}{2}} when ± is minus.

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

The equation is now solved.

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