Solve 10^2+x^2=24^2

$${ 10 }^{ 2 } + { x }^{ 2 } = { 24 }^{ 2 }$$

Solve for x

$$x=2\sqrt{119}\approx 21.817424229$$

$$x=-2\sqrt{119}\approx -21.817424229$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$100+x^{2}=24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$100+x^{2}=576$$

Subtract 100 from both sides.

$$x^{2}=576-100$$

Subtract 100 from 576 to get 476.

$$x^{2}=476$$

Take the square root of both sides of the equation.

$$x=2\sqrt{119} x=-2\sqrt{119}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$100+x^{2}=24^{2}$$

Calculate 24 to the power of 2 and get 576.

$$100+x^{2}=576$$

Subtract 576 from both sides.

$$100+x^{2}-576=0$$

Subtract 576 from 100 to get -476.

$$-476+x^{2}=0$$

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.

$$x^{2}-476=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -476 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-476\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-476\right)}}{2}$$

Multiply -4 times -476.

$$x=\frac{0±\sqrt{1904}}{2}$$

Take the square root of 1904.

$$x=\frac{0±4\sqrt{119}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{119}}{2} when ± is plus.

$$x=2\sqrt{119}$$

Now solve the equation x=\frac{0±4\sqrt{119}}{2} when ± is minus.

$$x=-2\sqrt{119}$$

The equation is now solved.

$$x=2\sqrt{119} x=-2\sqrt{119}$$