Solve x^2-1=1/2

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

Solve for x

$$x = \frac{\sqrt{6}}{2} \approx 1.224744871$$

$$x = -\frac{\sqrt{6}}{2} \approx -1.224744871$$

Steps by Finding Square Root

Add 1 to both sides.

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

Add \frac{1}{2} and 1 to get \frac{3}{2}.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{2} x=-\frac{\sqrt{6}}{2}$$

Steps Using the Quadratic Formula

Subtract \frac{1}{2} from both sides.

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

Subtract \frac{1}{2} from -1 to get -\frac{3}{2}.

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

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

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

Square 0.

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

Multiply -4 times -\frac{3}{2}.

$$x=\frac{0±\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±\sqrt{6}}{2} when ± is plus.

$$x=\frac{\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±\sqrt{6}}{2} when ± is minus.

$$x=-\frac{\sqrt{6}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{2} x=-\frac{\sqrt{6}}{2}$$