Solve x^2=60^2-40^2

$$x ^ { 2 } = 60 ^ { 2 } - 40 ^ { 2 }$$

Solve for x

$$x=20\sqrt{5}\approx 44.72135955$$

$$x=-20\sqrt{5}\approx -44.72135955$$

Steps by Finding Square Root

Calculate 60 to the power of 2 and get 3600.

$$x^{2}=3600-40^{2}$$

Calculate 40 to the power of 2 and get 1600.

$$x^{2}=3600-1600$$

Subtract 1600 from 3600 to get 2000.

$$x^{2}=2000$$

Take the square root of both sides of the equation.

$$x=20\sqrt{5} x=-20\sqrt{5}$$

Steps Using the Quadratic Formula

Calculate 60 to the power of 2 and get 3600.

$$x^{2}=3600-40^{2}$$

Calculate 40 to the power of 2 and get 1600.

$$x^{2}=3600-1600$$

Subtract 1600 from 3600 to get 2000.

$$x^{2}=2000$$

Subtract 2000 from both sides.

$$x^{2}-2000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -2000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2000\right)}}{2}$$

Multiply -4 times -2000.

$$x=\frac{0±\sqrt{8000}}{2}$$

Take the square root of 8000.

$$x=\frac{0±40\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±40\sqrt{5}}{2} when ± is plus.

$$x=20\sqrt{5}$$

Now solve the equation x=\frac{0±40\sqrt{5}}{2} when ± is minus.

$$x=-20\sqrt{5}$$

The equation is now solved.

$$x=20\sqrt{5} x=-20\sqrt{5}$$