Solve x^2+24+144=0

$$x ^ { 2 } + 24 + 144 = 0$$

Solve for x (complex solution)

$$x=-2\sqrt{42}i\approx -0-12.961481397i$$

$$x=2\sqrt{42}i\approx 12.961481397i$$

Steps by Finding Square Root

Add 24 and 144 to get 168.

$$x^{2}+168=0$$

Subtract 168 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-168$$

The equation is now solved.

$$x=2\sqrt{42}i x=-2\sqrt{42}i$$

Steps Using the Quadratic Formula

Add 24 and 144 to get 168.

$$x^{2}+168=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 168 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 168}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 168}}{2}$$

Multiply -4 times 168.

$$x=\frac{0±\sqrt{-672}}{2}$$

Take the square root of -672.

$$x=\frac{0±4\sqrt{42}i}{2}$$

Now solve the equation x=\frac{0±4\sqrt{42}i}{2} when ± is plus.

$$x=2\sqrt{42}i$$

Now solve the equation x=\frac{0±4\sqrt{42}i}{2} when ± is minus.

$$x=-2\sqrt{42}i$$

The equation is now solved.

$$x=2\sqrt{42}i x=-2\sqrt{42}i$$