Solve a^2-1=-1/2

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

Solve for a

$$a=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$a=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Steps by Finding Square Root

Add 1 to both sides.

$$a^{2}=-\frac{1}{2}+1$$

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

$$a^{2}=\frac{1}{2}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{2}}{2} a=-\frac{\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Add \frac{1}{2} to both sides.

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

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

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

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

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

Square 0.

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

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

$$a=\frac{0±\sqrt{2}}{2}$$

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

$$a=\frac{\sqrt{2}}{2}$$

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

$$a=-\frac{\sqrt{2}}{2}$$

The equation is now solved.

$$a=\frac{\sqrt{2}}{2} a=-\frac{\sqrt{2}}{2}$$