Solve 1/4+x^2=1

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

Solve for x

$$x=\frac{\sqrt{3}}{2}\approx 0.866025404$$

$$x=-\frac{\sqrt{3}}{2}\approx -0.866025404$$

Steps by Finding Square Root

Subtract \frac{1}{4} from both sides.

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

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$x^{2}=\frac{3}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{3}}{2} x=-\frac{\sqrt{3}}{2}$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

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

Subtract 1 from \frac{1}{4} to get -\frac{3}{4}.

$$-\frac{3}{4}+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-\frac{3}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{3}{4}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{3}{4}\right)}}{2}$$

Multiply -4 times -\frac{3}{4}.

$$x=\frac{0±\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±\sqrt{3}}{2} when ± is plus.

$$x=\frac{\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±\sqrt{3}}{2} when ± is minus.

$$x=-\frac{\sqrt{3}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{3}}{2} x=-\frac{\sqrt{3}}{2}$$