Solve H^2=12^2+5^2

$$H ^ { 2 } = 12 ^ { 2 } + 5 ^ { 2 }$$

Solve for H

$$H=-13$$

$$H=13$$

Steps Using Difference of Squares

Calculate 12 to the power of 2 and get 144.

$$H^{2}=144+5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$H^{2}=144+25$$

Add 144 and 25 to get 169.

$$H^{2}=169$$

Subtract 169 from both sides.

$$H^{2}-169=0$$

Consider H^{2}-169. Rewrite H^{2}-169 as H^{2}-13^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(H-13\right)\left(H+13\right)=0$$

To find equation solutions, solve H-13=0 and H+13=0.

$$H=13 H=-13$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$H^{2}=144+5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$H^{2}=144+25$$

Add 144 and 25 to get 169.

$$H^{2}=169$$

Take the square root of both sides of the equation.

$$H=13 H=-13$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$H^{2}=144+5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$H^{2}=144+25$$

Add 144 and 25 to get 169.

$$H^{2}=169$$

Subtract 169 from both sides.

$$H^{2}-169=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -169 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$H=\frac{0±\sqrt{0^{2}-4\left(-169\right)}}{2}$$

Square 0.

$$H=\frac{0±\sqrt{-4\left(-169\right)}}{2}$$

Multiply -4 times -169.

$$H=\frac{0±\sqrt{676}}{2}$$

Take the square root of 676.

$$H=\frac{0±26}{2}$$

Now solve the equation H=\frac{0±26}{2} when ± is plus. Divide 26 by 2.

$$H=13$$

Now solve the equation H=\frac{0±26}{2} when ± is minus. Divide -26 by 2.

$$H=-13$$

The equation is now solved.

$$H=13 H=-13$$