Solve h^2-120=3601

$$h ^ { 2 } - 120 = 3601$$

Solve for h

$$h=61$$

$$h=-61$$

Steps Using Difference of Squares

Subtract 3601 from both sides.

$$h^{2}-120-3601=0$$

Subtract 3601 from -120 to get -3721.

$$h^{2}-3721=0$$

Consider h^{2}-3721. Rewrite h^{2}-3721 as h^{2}-61^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(h-61\right)\left(h+61\right)=0$$

To find equation solutions, solve h-61=0 and h+61=0.

$$h=61 h=-61$$

Steps by Finding Square Root

Add 120 to both sides.

$$h^{2}=3601+120$$

Add 3601 and 120 to get 3721.

$$h^{2}=3721$$

Take the square root of both sides of the equation.

$$h=61 h=-61$$

Steps Using the Quadratic Formula

Subtract 3601 from both sides.

$$h^{2}-120-3601=0$$

Subtract 3601 from -120 to get -3721.

$$h^{2}-3721=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3721 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$h=\frac{0±\sqrt{0^{2}-4\left(-3721\right)}}{2}$$

Square 0.

$$h=\frac{0±\sqrt{-4\left(-3721\right)}}{2}$$

Multiply -4 times -3721.

$$h=\frac{0±\sqrt{14884}}{2}$$

Take the square root of 14884.

$$h=\frac{0±122}{2}$$

Now solve the equation h=\frac{0±122}{2} when ± is plus. Divide 122 by 2.

$$h=61$$

Now solve the equation h=\frac{0±122}{2} when ± is minus. Divide -122 by 2.

$$h=-61$$

The equation is now solved.

$$h=61 h=-61$$