Solve 2x^2+400=7

$$2 x ^ { 2 } + 400 = 7$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{786}i}{2}\approx -0-14.017845769i$$

$$x=\frac{\sqrt{786}i}{2}\approx 14.017845769i$$

Steps by Finding Square Root

Subtract 400 from both sides.

$$2x^{2}=7-400$$

Subtract 400 from 7 to get -393.

$$2x^{2}=-393$$

Divide both sides by 2.

$$x^{2}=-\frac{393}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{786}i}{2} x=-\frac{\sqrt{786}i}{2}$$

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$2x^{2}+400-7=0$$

Subtract 7 from 400 to get 393.

$$2x^{2}+393=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 393 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 393}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 393}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 393}}{2\times 2}$$

Multiply -8 times 393.

$$x=\frac{0±\sqrt{-3144}}{2\times 2}$$

Take the square root of -3144.

$$x=\frac{0±2\sqrt{786}i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±2\sqrt{786}i}{4}$$

Now solve the equation x=\frac{0±2\sqrt{786}i}{4} when ± is plus.

$$x=\frac{\sqrt{786}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{786}i}{4} when ± is minus.

$$x=-\frac{\sqrt{786}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{786}i}{2} x=-\frac{\sqrt{786}i}{2}$$