Solve 20^2+x^2=24^2

$$20 ^ { 2 } + x ^ { 2 } = 24 ^ { 2 }$$

Solve for x

$$x=4\sqrt{11}\approx 13.266499161$$

$$x=-4\sqrt{11}\approx -13.266499161$$

Steps by Finding Square Root

Calculate 20 to the power of 2 and get 400.

$$400+x^{2}=24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$400+x^{2}=576$$

Subtract 400 from both sides.

$$x^{2}=576-400$$

Subtract 400 from 576 to get 176.

$$x^{2}=176$$

Take the square root of both sides of the equation.

$$x=4\sqrt{11} x=-4\sqrt{11}$$

Steps Using the Quadratic Formula

Calculate 20 to the power of 2 and get 400.

$$400+x^{2}=24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$400+x^{2}=576$$

Subtract 576 from both sides.

$$400+x^{2}-576=0$$

Subtract 576 from 400 to get -176.

$$-176+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-176=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -176 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-176\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-176\right)}}{2}$$

Multiply -4 times -176.

$$x=\frac{0±\sqrt{704}}{2}$$

Take the square root of 704.

$$x=\frac{0±8\sqrt{11}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{11}}{2} when ± is plus.

$$x=4\sqrt{11}$$

Now solve the equation x=\frac{0±8\sqrt{11}}{2} when ± is minus.

$$x=-4\sqrt{11}$$

The equation is now solved.

$$x=4\sqrt{11} x=-4\sqrt{11}$$