Solve x^2-25+144=0

$$x ^ { 2 } - 25 + 144 = 0$$

Solve for x (complex solution)

$$x=-\sqrt{119}i\approx -0-10.908712115i$$

$$x=\sqrt{119}i\approx 10.908712115i$$

Steps by Finding Square Root

Add -25 and 144 to get 119.

$$x^{2}+119=0$$

Subtract 119 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-119$$

The equation is now solved.

$$x=\sqrt{119}i x=-\sqrt{119}i$$

Steps Using the Quadratic Formula

Add -25 and 144 to get 119.

$$x^{2}+119=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 119 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 119}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 119}}{2}$$

Multiply -4 times 119.

$$x=\frac{0±\sqrt{-476}}{2}$$

Take the square root of -476.

$$x=\frac{0±2\sqrt{119}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{119}i}{2} when ± is plus.

$$x=\sqrt{119}i$$

Now solve the equation x=\frac{0±2\sqrt{119}i}{2} when ± is minus.

$$x=-\sqrt{119}i$$

The equation is now solved.

$$x=\sqrt{119}i x=-\sqrt{119}i$$