Solve 12^2+x^2=15

$$12 ^ { 2 } + x ^ { 2 } = 15$$

Solve for x (complex solution)

$$x=-\sqrt{129}i\approx -0-11.357816692i$$

$$x=\sqrt{129}i\approx 11.357816692i$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$144+x^{2}=15$$

Subtract 144 from both sides.

$$x^{2}=15-144$$

Subtract 144 from 15 to get -129.

$$x^{2}=-129$$

The equation is now solved.

$$x=\sqrt{129}i x=-\sqrt{129}i$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$144+x^{2}=15$$

Subtract 15 from both sides.

$$144+x^{2}-15=0$$

Subtract 15 from 144 to get 129.

$$129+x^{2}=0$$

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.

$$x^{2}+129=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 129 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 129}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 129}}{2}$$

Multiply -4 times 129.

$$x=\frac{0±\sqrt{-516}}{2}$$

Take the square root of -516.

$$x=\frac{0±2\sqrt{129}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{129}i}{2} when ± is plus.

$$x=\sqrt{129}i$$

Now solve the equation x=\frac{0±2\sqrt{129}i}{2} when ± is minus.

$$x=-\sqrt{129}i$$

The equation is now solved.

$$x=\sqrt{129}i x=-\sqrt{129}i$$