Solve 10^2=x^2+x^2

$$10 ^ { 2 } = x ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x=5\sqrt{2}\approx 7.071067812$$

$$x=-5\sqrt{2}\approx -7.071067812$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$100=x^{2}+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$100=2x^{2}$$

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

$$2x^{2}=100$$

Divide both sides by 2.

$$x^{2}=\frac{100}{2}$$

Divide 100 by 2 to get 50.

$$x^{2}=50$$

Take the square root of both sides of the equation.

$$x=5\sqrt{2} x=-5\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$100=x^{2}+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$100=2x^{2}$$

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

$$2x^{2}=100$$

Subtract 100 from both sides.

$$2x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-100\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-100\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-100\right)}}{2\times 2}$$

Multiply -8 times -100.

$$x=\frac{0±\sqrt{800}}{2\times 2}$$

Take the square root of 800.

$$x=\frac{0±20\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±20\sqrt{2}}{4}$$

Now solve the equation x=\frac{0±20\sqrt{2}}{4} when ± is plus.

$$x=5\sqrt{2}$$

Now solve the equation x=\frac{0±20\sqrt{2}}{4} when ± is minus.

$$x=-5\sqrt{2}$$

The equation is now solved.

$$x=5\sqrt{2} x=-5\sqrt{2}$$