Solve 2x^2-14=0

$$2 { x }^{ 2 } -14=0$$

Solve for x

$$x=\sqrt{7}\approx 2.645751311$$

$$x=-\sqrt{7}\approx -2.645751311$$

Steps by Finding Square Root

Add 14 to both sides. Anything plus zero gives itself.

$$2x^{2}=14$$

Divide both sides by 2.

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

Divide 14 by 2 to get 7.

$$x^{2}=7$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$2x^{2}-14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-14\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-14\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-14\right)}}{2\times 2}$$

Multiply -8 times -14.

$$x=\frac{0±\sqrt{112}}{2\times 2}$$

Take the square root of 112.

$$x=\frac{0±4\sqrt{7}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{7}}{4}$$

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

$$x=\sqrt{7}$$

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

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

The equation is now solved.

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