Solve 8=4+16-c^2

$$8 = 4 + 16 - c ^ { 2 }$$

Solve for c

$$c=2\sqrt{3}\approx 3.464101615$$

$$c=-2\sqrt{3}\approx -3.464101615$$

Steps by Finding Square Root

Add 4 and 16 to get 20.

$$8=20-c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$20-c^{2}=8$$

Subtract 20 from both sides.

$$-c^{2}=8-20$$

Subtract 20 from 8 to get -12.

$$-c^{2}=-12$$

Divide both sides by -1.

$$c^{2}=\frac{-12}{-1}$$

Fraction \frac{-12}{-1} can be simplified to 12 by removing the negative sign from both the numerator and the denominator.

$$c^{2}=12$$

Take the square root of both sides of the equation.

$$c=2\sqrt{3} c=-2\sqrt{3}$$

Steps Using the Quadratic Formula

Add 4 and 16 to get 20.

$$8=20-c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$20-c^{2}=8$$

Subtract 8 from both sides.

$$20-c^{2}-8=0$$

Subtract 8 from 20 to get 12.

$$12-c^{2}=0$$

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.

$$-c^{2}+12=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 12 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

Square 0.

$$c=\frac{0±\sqrt{-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$c=\frac{0±\sqrt{4\times 12}}{2\left(-1\right)}$$

Multiply 4 times 12.

$$c=\frac{0±\sqrt{48}}{2\left(-1\right)}$$

Take the square root of 48.

$$c=\frac{0±4\sqrt{3}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$c=\frac{0±4\sqrt{3}}{-2}$$

Now solve the equation c=\frac{0±4\sqrt{3}}{-2} when ± is plus.

$$c=-2\sqrt{3}$$

Now solve the equation c=\frac{0±4\sqrt{3}}{-2} when ± is minus.

$$c=2\sqrt{3}$$

The equation is now solved.

$$c=-2\sqrt{3} c=2\sqrt{3}$$