Solve 2x^2-4=7

$$2 x ^ { 2 } - 4 = 7$$

Solve for x

$$x = \frac{\sqrt{22}}{2} \approx 2.34520788$$

$$x = -\frac{\sqrt{22}}{2} \approx -2.34520788$$

Steps by Finding Square Root

Add 4 to both sides.

$$2x^{2}=7+4$$

Add 7 and 4 to get 11.

$$2x^{2}=11$$

Divide both sides by 2.

$$x^{2}=\frac{11}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{22}}{2} x=-\frac{\sqrt{22}}{2}$$

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$2x^{2}-4-7=0$$

Subtract 7 from -4 to get -11.

$$2x^{2}-11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-11\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-11\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-11\right)}}{2\times 2}$$

Multiply -8 times -11.

$$x=\frac{0±\sqrt{88}}{2\times 2}$$

Take the square root of 88.

$$x=\frac{0±2\sqrt{22}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{22}}{4}$$

Now solve the equation x=\frac{0±2\sqrt{22}}{4} when ± is plus.

$$x=\frac{\sqrt{22}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{22}}{4} when ± is minus.

$$x=-\frac{\sqrt{22}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{22}}{2} x=-\frac{\sqrt{22}}{2}$$