Solve 11^2+10^2=x^2

$$11 ^ { 2 } + 10 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=\sqrt{221}\approx 14.866068747$$

$$x=-\sqrt{221}\approx -14.866068747$$

Steps by Finding Square Root

Calculate 11 to the power of 2 and get 121.

$$121+10^{2}=x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$121+100=x^{2}$$

Add 121 and 100 to get 221.

$$221=x^{2}$$

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

$$x^{2}=221$$

Take the square root of both sides of the equation.

$$x=\sqrt{221} x=-\sqrt{221}$$

Steps Using the Quadratic Formula

Calculate 11 to the power of 2 and get 121.

$$121+10^{2}=x^{2}$$

Calculate 10 to the power of 2 and get 100.

$$121+100=x^{2}$$

Add 121 and 100 to get 221.

$$221=x^{2}$$

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

$$x^{2}=221$$

Subtract 221 from both sides.

$$x^{2}-221=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -221 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-221\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-221\right)}}{2}$$

Multiply -4 times -221.

$$x=\frac{0±\sqrt{884}}{2}$$

Take the square root of 884.

$$x=\frac{0±2\sqrt{221}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{221}}{2} when ± is plus.

$$x=\sqrt{221}$$

Now solve the equation x=\frac{0±2\sqrt{221}}{2} when ± is minus.

$$x=-\sqrt{221}$$

The equation is now solved.

$$x=\sqrt{221} x=-\sqrt{221}$$