Solve 2x^2-3=1/2

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

Solve for x

$$x = \frac{\sqrt{7}}{2} \approx 1.322875656$$

$$x = -\frac{\sqrt{7}}{2} \approx -1.322875656$$

Steps by Finding Square Root

Add 3 to both sides.

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

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

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

Divide both sides by 2.

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

Express \frac{\frac{7}{2}}{2} as a single fraction.

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

Multiply 2 and 2 to get 4.

$$x^{2}=\frac{7}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{7}}{2} x=-\frac{\sqrt{7}}{2}$$

Steps Using the Quadratic Formula

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

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

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

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-\frac{7}{2}\right)}}{2\times 2}$$

Multiply -8 times -\frac{7}{2}.

$$x=\frac{0±\sqrt{28}}{2\times 2}$$

Take the square root of 28.

$$x=\frac{0±2\sqrt{7}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{7}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{7}}{4} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{7}}{4} when ± is minus.

$$x=-\frac{\sqrt{7}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{7}}{2} x=-\frac{\sqrt{7}}{2}$$