Solve 2x^2+7=1

$$2 x ^ { 2 } + 7 = 1$$

Solve for x (complex solution)

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

$$x=\sqrt{3}i\approx 1.732050808i$$

Steps by Finding Square Root

Subtract 7 from both sides.

$$2x^{2}=1-7$$

Subtract 7 from 1 to get -6.

$$2x^{2}=-6$$

Divide both sides by 2.

$$x^{2}=\frac{-6}{2}$$

Divide -6 by 2 to get -3.

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

The equation is now solved.

$$x=\sqrt{3}i x=-\sqrt{3}i$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$2x^{2}+7-1=0$$

Subtract 1 from 7 to get 6.

$$2x^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 6}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 6}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 6}}{2\times 2}$$

Multiply -8 times 6.

$$x=\frac{0±\sqrt{-48}}{2\times 2}$$

Take the square root of -48.

$$x=\frac{0±4\sqrt{3}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{3}i}{4}$$

Now solve the equation x=\frac{0±4\sqrt{3}i}{4} when ± is plus.

$$x=\sqrt{3}i$$

Now solve the equation x=\frac{0±4\sqrt{3}i}{4} when ± is minus.

$$x=-\sqrt{3}i$$

The equation is now solved.

$$x=\sqrt{3}i x=-\sqrt{3}i$$