Solve a^2=84

$$a ^ { 2 } = 84$$

Solve for a

$$a=2\sqrt{21}\approx 9.16515139$$

$$a=-2\sqrt{21}\approx -9.16515139$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$a=2\sqrt{21} a=-2\sqrt{21}$$

Steps Using the Quadratic Formula

Subtract 84 from both sides.

$$a^{2}-84=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -84 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-84\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-84\right)}}{2}$$

Multiply -4 times -84.

$$a=\frac{0±\sqrt{336}}{2}$$

Take the square root of 336.

$$a=\frac{0±4\sqrt{21}}{2}$$

Now solve the equation a=\frac{0±4\sqrt{21}}{2} when ± is plus.

$$a=2\sqrt{21}$$

Now solve the equation a=\frac{0±4\sqrt{21}}{2} when ± is minus.

$$a=-2\sqrt{21}$$

The equation is now solved.

$$a=2\sqrt{21} a=-2\sqrt{21}$$