Solve x^2-1/2=3

$$x ^ { 2 } - \frac { 1 } { 2 } = 3$$

Solve for x

$$x = \frac{\sqrt{14}}{2} \approx 1.870828693$$

$$x = -\frac{\sqrt{14}}{2} \approx -1.870828693$$

Steps by Finding Square Root

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

$$x^{2}=3+\frac{1}{2}$$

Add 3 and \frac{1}{2} to get \frac{7}{2}.

$$x^{2}=\frac{7}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{14}}{2} x=-\frac{\sqrt{14}}{2}$$

Steps Using the Quadratic Formula

Subtract 3 from both sides.

$$x^{2}-\frac{1}{2}-3=0$$

Subtract 3 from -\frac{1}{2} to get -\frac{7}{2}.

$$x^{2}-\frac{7}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{7}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{7}{2}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{7}{2}\right)}}{2}$$

Multiply -4 times -\frac{7}{2}.

$$x=\frac{0±\sqrt{14}}{2}$$

Now solve the equation x=\frac{0±\sqrt{14}}{2} when ± is plus.

$$x=\frac{\sqrt{14}}{2}$$

Now solve the equation x=\frac{0±\sqrt{14}}{2} when ± is minus.

$$x=-\frac{\sqrt{14}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{14}}{2} x=-\frac{\sqrt{14}}{2}$$