Solve 2x^2+8=7

$$2 x ^ { 2 } + 8 = 7$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}i}{2}\approx -0-0.707106781i$$

$$x=\frac{\sqrt{2}i}{2}\approx 0.707106781i$$

Steps by Finding Square Root

Subtract 8 from both sides.

$$2x^{2}=7-8$$

Subtract 8 from 7 to get -1.

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

Divide both sides by 2.

$$x^{2}=-\frac{1}{2}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$2x^{2}+8-7=0$$

Subtract 7 from 8 to get 1.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8}}{2\times 2}$$

Take the square root of -8.

$$x=\frac{0±2\sqrt{2}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{2}i}{4}$$

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

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

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

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

The equation is now solved.

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