Solve 30^2=18^2+x^2

$$30 ^ { 2 } = 18 ^ { 2 } + x ^ { 2 }$$

Solve for x

$$x=24$$

$$x=-24$$

Steps Using Difference of Squares

Calculate 30 to the power of 2 and get 900.

$$900=18^{2}+x^{2}$$

Calculate 18 to the power of 2 and get 324.

$$900=324+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$324+x^{2}=900$$

Subtract 900 from both sides.

$$324+x^{2}-900=0$$

Subtract 900 from 324 to get -576.

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

Consider -576+x^{2}. Rewrite -576+x^{2} as x^{2}-24^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-24\right)\left(x+24\right)=0$$

To find equation solutions, solve x-24=0 and x+24=0.

$$x=24 x=-24$$

Steps by Finding Square Root

Calculate 30 to the power of 2 and get 900.

$$900=18^{2}+x^{2}$$

Calculate 18 to the power of 2 and get 324.

$$900=324+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$324+x^{2}=900$$

Subtract 324 from both sides.

$$x^{2}=900-324$$

Subtract 324 from 900 to get 576.

$$x^{2}=576$$

Take the square root of both sides of the equation.

$$x=24 x=-24$$

Steps Using the Quadratic Formula

Calculate 30 to the power of 2 and get 900.

$$900=18^{2}+x^{2}$$

Calculate 18 to the power of 2 and get 324.

$$900=324+x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$324+x^{2}=900$$

Subtract 900 from both sides.

$$324+x^{2}-900=0$$

Subtract 900 from 324 to get -576.

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

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-576\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-576\right)}}{2}$$

Multiply -4 times -576.

$$x=\frac{0±\sqrt{2304}}{2}$$

Take the square root of 2304.

$$x=\frac{0±48}{2}$$

Now solve the equation x=\frac{0±48}{2} when ± is plus. Divide 48 by 2.

$$x=24$$

Now solve the equation x=\frac{0±48}{2} when ± is minus. Divide -48 by 2.

$$x=-24$$

The equation is now solved.

$$x=24 x=-24$$