Solve 2x^2-4=8

$$2 x ^ { 2 } - 4 = 8$$

Solve for x

$$x=\sqrt{6}\approx 2.449489743$$

$$x=-\sqrt{6}\approx -2.449489743$$

Steps by Finding Square Root

Add 4 to both sides.

$$2x^{2}=8+4$$

Add 8 and 4 to get 12.

$$2x^{2}=12$$

Divide both sides by 2.

$$x^{2}=\frac{12}{2}$$

Divide 12 by 2 to get 6.

$$x^{2}=6$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Subtract 8 from both sides.

$$2x^{2}-4-8=0$$

Subtract 8 from -4 to get -12.

$$2x^{2}-12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-12\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-12\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-12\right)}}{2\times 2}$$

Multiply -8 times -12.

$$x=\frac{0±\sqrt{96}}{2\times 2}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{6}}{4}$$

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

$$x=\sqrt{6}$$

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

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

The equation is now solved.

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