Solve a^2=120+20

$$a ^ { 2 } = 120 + 20$$

Solve for a

$$a=2\sqrt{35}\approx 11.832159566$$

$$a=-2\sqrt{35}\approx -11.832159566$$

Steps by Finding Square Root

Add 120 and 20 to get 140.

$$a^{2}=140$$

Take the square root of both sides of the equation.

$$a=2\sqrt{35} a=-2\sqrt{35}$$

Steps Using the Quadratic Formula

Add 120 and 20 to get 140.

$$a^{2}=140$$

Subtract 140 from both sides.

$$a^{2}-140=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -140 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-140\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-140\right)}}{2}$$

Multiply -4 times -140.

$$a=\frac{0±\sqrt{560}}{2}$$

Take the square root of 560.

$$a=\frac{0±4\sqrt{35}}{2}$$

Now solve the equation a=\frac{0±4\sqrt{35}}{2} when ± is plus.

$$a=2\sqrt{35}$$

Now solve the equation a=\frac{0±4\sqrt{35}}{2} when ± is minus.

$$a=-2\sqrt{35}$$

The equation is now solved.

$$a=2\sqrt{35} a=-2\sqrt{35}$$