Solve 2x^2-9=-209

$$2 x ^ { 2 } - 9 = - 209$$

Solve for x (complex solution)

$$x=-10i$$

$$x=10i$$

Steps by Finding Square Root

Add 9 to both sides.

$$2x^{2}=-209+9$$

Add -209 and 9 to get -200.

$$2x^{2}=-200$$

Divide both sides by 2.

$$x^{2}=\frac{-200}{2}$$

Divide -200 by 2 to get -100.

$$x^{2}=-100$$

The equation is now solved.

$$x=10i x=-10i$$

Steps Using the Quadratic Formula

Add 209 to both sides.

$$2x^{2}-9+209=0$$

Add -9 and 209 to get 200.

$$2x^{2}+200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 200}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 200}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 200}}{2\times 2}$$

Multiply -8 times 200.

$$x=\frac{0±\sqrt{-1600}}{2\times 2}$$

Take the square root of -1600.

$$x=\frac{0±40i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±40i}{4}$$

Now solve the equation x=\frac{0±40i}{4} when ± is plus.

$$x=10i$$

Now solve the equation x=\frac{0±40i}{4} when ± is minus.

$$x=-10i$$

The equation is now solved.

$$x=10i x=-10i$$