Solve 2x^2+1=4

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

Solve for x

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

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

Steps by Finding Square Root

Subtract 1 from both sides.

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

Subtract 1 from 4 to get 3.

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

Divide both sides by 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 4 from both sides.

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

Subtract 4 from 1 to get -3.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-3\right)}}{2\times 2}$$

Multiply -8 times -3.

$$x=\frac{0±\sqrt{24}}{2\times 2}$$

Take the square root of 24.

$$x=\frac{0±2\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{6}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{6}}{4} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{6}}{4} when ± is minus.

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

The equation is now solved.

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