Solve 2x^2+3=16

$$2 x ^ { 2 } + 3 = 16$$

Solve for x

$$x = \frac{\sqrt{26}}{2} \approx 2.549509757$$

$$x = -\frac{\sqrt{26}}{2} \approx -2.549509757$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$2x^{2}=16-3$$

Subtract 3 from 16 to get 13.

$$2x^{2}=13$$

Divide both sides by 2.

$$x^{2}=\frac{13}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{26}}{2} x=-\frac{\sqrt{26}}{2}$$

Steps Using the Quadratic Formula

Subtract 16 from both sides.

$$2x^{2}+3-16=0$$

Subtract 16 from 3 to get -13.

$$2x^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-13\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-13\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-13\right)}}{2\times 2}$$

Multiply -8 times -13.

$$x=\frac{0±\sqrt{104}}{2\times 2}$$

Take the square root of 104.

$$x=\frac{0±2\sqrt{26}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{26}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{26}}{4} when ± is plus.

$$x=\frac{\sqrt{26}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{26}}{4} when ± is minus.

$$x=-\frac{\sqrt{26}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{26}}{2} x=-\frac{\sqrt{26}}{2}$$