Solve k^2+4=24

$$k ^ { 2 } + 4 = 24$$

Solve for k

$$k=2\sqrt{5}\approx 4.472135955$$

$$k=-2\sqrt{5}\approx -4.472135955$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$k^{2}=24-4$$

Subtract 4 from 24 to get 20.

$$k^{2}=20$$

Take the square root of both sides of the equation.

$$k=2\sqrt{5} k=-2\sqrt{5}$$

Steps Using the Quadratic Formula

Subtract 24 from both sides.

$$k^{2}+4-24=0$$

Subtract 24 from 4 to get -20.

$$k^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$k=\frac{0±\sqrt{0^{2}-4\left(-20\right)}}{2}$$

Square 0.

$$k=\frac{0±\sqrt{-4\left(-20\right)}}{2}$$

Multiply -4 times -20.

$$k=\frac{0±\sqrt{80}}{2}$$

Take the square root of 80.

$$k=\frac{0±4\sqrt{5}}{2}$$

Now solve the equation k=\frac{0±4\sqrt{5}}{2} when ± is plus.

$$k=2\sqrt{5}$$

Now solve the equation k=\frac{0±4\sqrt{5}}{2} when ± is minus.

$$k=-2\sqrt{5}$$

The equation is now solved.

$$k=2\sqrt{5} k=-2\sqrt{5}$$