Solve a^2+40^2=75^2

$$a ^ { 2 } + 40 ^ { 2 } = 75 ^ { 2 }$$

Solve for a

$$a=5\sqrt{161}\approx 63.442887702$$

$$a=-5\sqrt{161}\approx -63.442887702$$

Steps by Finding Square Root

Calculate 40 to the power of 2 and get 1600.

$$a^{2}+1600=75^{2}$$

Calculate 75 to the power of 2 and get 5625.

$$a^{2}+1600=5625$$

Subtract 1600 from both sides.

$$a^{2}=5625-1600$$

Subtract 1600 from 5625 to get 4025.

$$a^{2}=4025$$

Take the square root of both sides of the equation.

$$a=5\sqrt{161} a=-5\sqrt{161}$$

Steps Using the Quadratic Formula

Calculate 40 to the power of 2 and get 1600.

$$a^{2}+1600=75^{2}$$

Calculate 75 to the power of 2 and get 5625.

$$a^{2}+1600=5625$$

Subtract 5625 from both sides.

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

Subtract 5625 from 1600 to get -4025.

$$a^{2}-4025=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4025 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-4025\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-4025\right)}}{2}$$

Multiply -4 times -4025.

$$a=\frac{0±\sqrt{16100}}{2}$$

Take the square root of 16100.

$$a=\frac{0±10\sqrt{161}}{2}$$

Now solve the equation a=\frac{0±10\sqrt{161}}{2} when ± is plus.

$$a=5\sqrt{161}$$

Now solve the equation a=\frac{0±10\sqrt{161}}{2} when ± is minus.

$$a=-5\sqrt{161}$$

The equation is now solved.

$$a=5\sqrt{161} a=-5\sqrt{161}$$