Solve 615+x^2=2

$$615 + x ^ { 2 } = 2$$

Solve for x (complex solution)

$$x=-\sqrt{613}i\approx -0-24.758836806i$$

$$x=\sqrt{613}i\approx 24.758836806i$$

Steps by Finding Square Root

Subtract 615 from both sides.

$$x^{2}=2-615$$

Subtract 615 from 2 to get -613.

$$x^{2}=-613$$

The equation is now solved.

$$x=\sqrt{613}i x=-\sqrt{613}i$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$615+x^{2}-2=0$$

Subtract 2 from 615 to get 613.

$$613+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}+613=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 613 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 613}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 613}}{2}$$

Multiply -4 times 613.

$$x=\frac{0±\sqrt{-2452}}{2}$$

Take the square root of -2452.

$$x=\frac{0±2\sqrt{613}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{613}i}{2} when ± is plus.

$$x=\sqrt{613}i$$

Now solve the equation x=\frac{0±2\sqrt{613}i}{2} when ± is minus.

$$x=-\sqrt{613}i$$

The equation is now solved.

$$x=\sqrt{613}i x=-\sqrt{613}i$$