Solve 9^2+x^2=15^2

$$9 ^ { 2 } + x ^ { 2 } = 15 ^ { 2 }$$

Solve for x

$$x=-12$$

$$x=12$$

Steps Using Difference of Squares

Calculate 9 to the power of 2 and get 81.

$$81+x^{2}=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$81+x^{2}=225$$

Subtract 225 from both sides.

$$81+x^{2}-225=0$$

Subtract 225 from 81 to get -144.

$$-144+x^{2}=0$$

Consider -144+x^{2}. Rewrite -144+x^{2} as x^{2}-12^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-12\right)\left(x+12\right)=0$$

To find equation solutions, solve x-12=0 and x+12=0.

$$x=12 x=-12$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$81+x^{2}=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$81+x^{2}=225$$

Subtract 81 from both sides.

$$x^{2}=225-81$$

Subtract 81 from 225 to get 144.

$$x^{2}=144$$

Take the square root of both sides of the equation.

$$x=12 x=-12$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$81+x^{2}=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$81+x^{2}=225$$

Subtract 225 from both sides.

$$81+x^{2}-225=0$$

Subtract 225 from 81 to get -144.

$$-144+x^{2}=0$$

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.

$$x^{2}-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-144\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-144\right)}}{2}$$

Multiply -4 times -144.

$$x=\frac{0±\sqrt{576}}{2}$$

Take the square root of 576.

$$x=\frac{0±24}{2}$$

Now solve the equation x=\frac{0±24}{2} when ± is plus. Divide 24 by 2.

$$x=12$$

Now solve the equation x=\frac{0±24}{2} when ± is minus. Divide -24 by 2.

$$x=-12$$

The equation is now solved.

$$x=12 x=-12$$