Solve 12^5+x^2=0

$$12 ^ { 5 } + x ^ { 2 } = 0$$

Solve for x (complex solution)

$$x=-288\sqrt{3}i\approx -0-498.83063258i$$

$$x=288\sqrt{3}i\approx 498.83063258i$$

Steps by Finding Square Root

Calculate 12 to the power of 5 and get 248832.

$$248832+x^{2}=0$$

Subtract 248832 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}=-248832$$

The equation is now solved.

$$x=288\sqrt{3}i x=-288\sqrt{3}i$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 5 and get 248832.

$$248832+x^{2}=0$$

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.

$$x^{2}+248832=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 248832 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 248832}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 248832}}{2}$$

Multiply -4 times 248832.

$$x=\frac{0±\sqrt{-995328}}{2}$$

Take the square root of -995328.

$$x=\frac{0±576\sqrt{3}i}{2}$$

Now solve the equation x=\frac{0±576\sqrt{3}i}{2} when ± is plus.

$$x=288\sqrt{3}i$$

Now solve the equation x=\frac{0±576\sqrt{3}i}{2} when ± is minus.

$$x=-288\sqrt{3}i$$

The equation is now solved.

$$x=288\sqrt{3}i x=-288\sqrt{3}i$$