Solve 12^2+x^2=15^2

$$12 ^ { 2 } + x ^ { 2 } = 15 ^ { 2 }$$

Solve for x

$$x=-9$$

$$x=9$$

Steps Using Difference of Squares

Calculate 12 to the power of 2 and get 144.

$$144+x^{2}=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$144+x^{2}=225$$

Subtract 225 from both sides.

$$144+x^{2}-225=0$$

Subtract 225 from 144 to get -81.

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

Consider -81+x^{2}. Rewrite -81+x^{2} as x^{2}-9^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-9\right)\left(x+9\right)=0$$

To find equation solutions, solve x-9=0 and x+9=0.

$$x=9 x=-9$$

Steps by Finding Square Root

Calculate 12 to the power of 2 and get 144.

$$144+x^{2}=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$144+x^{2}=225$$

Subtract 144 from both sides.

$$x^{2}=225-144$$

Subtract 144 from 225 to get 81.

$$x^{2}=81$$

Take the square root of both sides of the equation.

$$x=9 x=-9$$

Steps Using the Quadratic Formula

Calculate 12 to the power of 2 and get 144.

$$144+x^{2}=15^{2}$$

Calculate 15 to the power of 2 and get 225.

$$144+x^{2}=225$$

Subtract 225 from both sides.

$$144+x^{2}-225=0$$

Subtract 225 from 144 to get -81.

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

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-81\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-81\right)}}{2}$$

Multiply -4 times -81.

$$x=\frac{0±\sqrt{324}}{2}$$

Take the square root of 324.

$$x=\frac{0±18}{2}$$

Now solve the equation x=\frac{0±18}{2} when ± is plus. Divide 18 by 2.

$$x=9$$

Now solve the equation x=\frac{0±18}{2} when ± is minus. Divide -18 by 2.

$$x=-9$$

The equation is now solved.

$$x=9 x=-9$$