Solve x^2=50^2+50^2

$$x ^ { 2 } = 50 ^ { 2 } + 50 ^ { 2 }$$

Solve for x

$$x=50\sqrt{2}\approx 70.710678119$$

$$x=-50\sqrt{2}\approx -70.710678119$$

Steps by Finding Square Root

Calculate 50 to the power of 2 and get 2500.

$$x^{2}=2500+50^{2}$$

Calculate 50 to the power of 2 and get 2500.

$$x^{2}=2500+2500$$

Add 2500 and 2500 to get 5000.

$$x^{2}=5000$$

Take the square root of both sides of the equation.

$$x=50\sqrt{2} x=-50\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 50 to the power of 2 and get 2500.

$$x^{2}=2500+50^{2}$$

Calculate 50 to the power of 2 and get 2500.

$$x^{2}=2500+2500$$

Add 2500 and 2500 to get 5000.

$$x^{2}=5000$$

Subtract 5000 from both sides.

$$x^{2}-5000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5000\right)}}{2}$$

Multiply -4 times -5000.

$$x=\frac{0±\sqrt{20000}}{2}$$

Take the square root of 20000.

$$x=\frac{0±100\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±100\sqrt{2}}{2} when ± is plus.

$$x=50\sqrt{2}$$

Now solve the equation x=\frac{0±100\sqrt{2}}{2} when ± is minus.

$$x=-50\sqrt{2}$$

The equation is now solved.

$$x=50\sqrt{2} x=-50\sqrt{2}$$