Solve 199^2+199^2=x^2

$$199 ^ { 2 } + 199 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=199\sqrt{2}\approx 281.428498912$$

$$x=-199\sqrt{2}\approx -281.428498912$$

Steps by Finding Square Root

Calculate 199 to the power of 2 and get 39601.

$$39601+199^{2}=x^{2}$$

Calculate 199 to the power of 2 and get 39601.

$$39601+39601=x^{2}$$

Add 39601 and 39601 to get 79202.

$$79202=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=79202$$

Take the square root of both sides of the equation.

$$x=199\sqrt{2} x=-199\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 199 to the power of 2 and get 39601.

$$39601+199^{2}=x^{2}$$

Calculate 199 to the power of 2 and get 39601.

$$39601+39601=x^{2}$$

Add 39601 and 39601 to get 79202.

$$79202=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=79202$$

Subtract 79202 from both sides.

$$x^{2}-79202=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -79202 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-79202\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-79202\right)}}{2}$$

Multiply -4 times -79202.

$$x=\frac{0±\sqrt{316808}}{2}$$

Take the square root of 316808.

$$x=\frac{0±398\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±398\sqrt{2}}{2} when ± is plus.

$$x=199\sqrt{2}$$

Now solve the equation x=\frac{0±398\sqrt{2}}{2} when ± is minus.

$$x=-199\sqrt{2}$$

The equation is now solved.

$$x=199\sqrt{2} x=-199\sqrt{2}$$