Solve a^2+53^2=85^2

$$a ^ { 2 } + 53 ^ { 2 } = 85 ^ { 2 }$$

Solve for a

$$a=8\sqrt{69}\approx 66.452990903$$

$$a=-8\sqrt{69}\approx -66.452990903$$

Steps by Finding Square Root

Calculate 53 to the power of 2 and get 2809.

$$a^{2}+2809=85^{2}$$

Calculate 85 to the power of 2 and get 7225.

$$a^{2}+2809=7225$$

Subtract 2809 from both sides.

$$a^{2}=7225-2809$$

Subtract 2809 from 7225 to get 4416.

$$a^{2}=4416$$

Take the square root of both sides of the equation.

$$a=8\sqrt{69} a=-8\sqrt{69}$$

Steps Using the Quadratic Formula

Calculate 53 to the power of 2 and get 2809.

$$a^{2}+2809=85^{2}$$

Calculate 85 to the power of 2 and get 7225.

$$a^{2}+2809=7225$$

Subtract 7225 from both sides.

$$a^{2}[phone]=0$$

Subtract 7225 from 2809 to get -4416.

$$a^{2}-4416=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4416 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-4416\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-4416\right)}}{2}$$

Multiply -4 times -4416.

$$a=\frac{0±\sqrt{17664}}{2}$$

Take the square root of 17664.

$$a=\frac{0±16\sqrt{69}}{2}$$

Now solve the equation a=\frac{0±16\sqrt{69}}{2} when ± is plus.

$$a=8\sqrt{69}$$

Now solve the equation a=\frac{0±16\sqrt{69}}{2} when ± is minus.

$$a=-8\sqrt{69}$$

The equation is now solved.

$$a=8\sqrt{69} a=-8\sqrt{69}$$