Solve 32+k^2=18

$$32 + k ^ { 2 } = 18$$

Solve for k

$$k=-\sqrt{14}i\approx -0-3.741657387i$$

$$k=\sqrt{14}i\approx 3.741657387i$$

Steps by Finding Square Root

Subtract 32 from both sides.

$$k^{2}=18-32$$

Subtract 32 from 18 to get -14.

$$k^{2}=-14$$

The equation is now solved.

$$k=\sqrt{14}i k=-\sqrt{14}i$$

Steps Using the Quadratic Formula

Subtract 18 from both sides.

$$32+k^{2}-18=0$$

Subtract 18 from 32 to get 14.

$$14+k^{2}=0$$

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.

$$k^{2}+14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\times 14}}{2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\times 14}}{2}$$

Multiply -4 times 14.

$$k=\frac{0±\sqrt{-56}}{2}$$

Take the square root of -56.

$$k=\frac{0±2\sqrt{14}i}{2}$$

Now solve the equation k=\frac{0±2\sqrt{14}i}{2} when ± is plus.

$$k=\sqrt{14}i$$

Now solve the equation k=\frac{0±2\sqrt{14}i}{2} when ± is minus.

$$k=-\sqrt{14}i$$

The equation is now solved.

$$k=\sqrt{14}i k=-\sqrt{14}i$$