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

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

Solve for x (complex solution)

$$x=-\sqrt{21}i\approx -0-4.582575695i$$

$$x=\sqrt{21}i\approx 4.582575695i$$

Steps by Finding Square Root

Calculate 11 to the power of 2 and get 121.

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

Calculate 10 to the power of 2 and get 100.

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

Subtract 121 from both sides.

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

Subtract 121 from 100 to get -21.

$$x^{2}=-21$$

The equation is now solved.

$$x=\sqrt{21}i x=-\sqrt{21}i$$

Steps Using the Quadratic Formula

Calculate 11 to the power of 2 and get 121.

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

Calculate 10 to the power of 2 and get 100.

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

Subtract 100 from both sides.

$$x^{2}+121-100=0$$

Subtract 100 from 121 to get 21.

$$x^{2}+21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 21}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 21}}{2}$$

Multiply -4 times 21.

$$x=\frac{0±\sqrt{-84}}{2}$$

Take the square root of -84.

$$x=\frac{0±2\sqrt{21}i}{2}$$

Now solve the equation x=\frac{0±2\sqrt{21}i}{2} when ± is plus.

$$x=\sqrt{21}i$$

Now solve the equation x=\frac{0±2\sqrt{21}i}{2} when ± is minus.

$$x=-\sqrt{21}i$$

The equation is now solved.

$$x=\sqrt{21}i x=-\sqrt{21}i$$