Solve x^2+110^2=220^2

$$x ^ { 2 } + 110 ^ { 2 } = 220 ^ { 2 }$$

Solve for x

$$x=110\sqrt{3}\approx 190.525588833$$

$$x=-110\sqrt{3}\approx -190.525588833$$

Steps by Finding Square Root

Calculate 110 to the power of 2 and get 12100.

$$x^{2}+12100=220^{2}$$

Calculate 220 to the power of 2 and get 48400.

$$x^{2}+12100=48400$$

Subtract 12100 from both sides.

$$x^{2}=48400-12100$$

Subtract 12100 from 48400 to get 36300.

$$x^{2}=36300$$

Take the square root of both sides of the equation.

$$x=110\sqrt{3} x=-110\sqrt{3}$$

Steps Using the Quadratic Formula

Calculate 110 to the power of 2 and get 12100.

$$x^{2}+12100=220^{2}$$

Calculate 220 to the power of 2 and get 48400.

$$x^{2}+12100=48400$$

Subtract 48400 from both sides.

$$x^{2}[phone]=0$$

Subtract 48400 from 12100 to get -36300.

$$x^{2}-36300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36300\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36300\right)}}{2}$$

Multiply -4 times -36300.

$$x=\frac{0±\sqrt{145200}}{2}$$

Take the square root of 145200.

$$x=\frac{0±220\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±220\sqrt{3}}{2} when ± is plus.

$$x=110\sqrt{3}$$

Now solve the equation x=\frac{0±220\sqrt{3}}{2} when ± is minus.

$$x=-110\sqrt{3}$$

The equation is now solved.

$$x=110\sqrt{3} x=-110\sqrt{3}$$