Solve x^2=12^2+20^2

$${ x }^{ 2 } = { 12 }^{ 2 } + { 20 }^{ 2 }$$

Solve for x

$$x=4\sqrt{34}\approx 23.323807579$$

$$x=-4\sqrt{34}\approx -23.323807579$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$x^{2}=144+20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=144+400$$

Add 144 and 400 to get 544.

$$x^{2}=544$$

Take the square root of both sides of the equation.

$$x=4\sqrt{34} x=-4\sqrt{34}$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$x^{2}=144+20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}=144+400$$

Add 144 and 400 to get 544.

$$x^{2}=544$$

Subtract 544 from both sides.

$$x^{2}-544=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -544 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-544\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-544\right)}}{2}$$

Multiply -4 times -544.

$$x=\frac{0±\sqrt{2176}}{2}$$

Take the square root of 2176.

$$x=\frac{0±8\sqrt{34}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{34}}{2} when ± is plus.

$$x=4\sqrt{34}$$

Now solve the equation x=\frac{0±8\sqrt{34}}{2} when ± is minus.

$$x=-4\sqrt{34}$$

The equation is now solved.

$$x=4\sqrt{34} x=-4\sqrt{34}$$