Solve 9^2+x^2=12^2

$${ 9 }^{ 2 } + { x }^{ 2 } = { 12 }^{ 2 }$$

Solve for x

$$x=3\sqrt{7}\approx 7.937253933$$

$$x=-3\sqrt{7}\approx -7.937253933$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$81+x^{2}=12^{2}$$

Calculate 12 to the power of 2 and get 144.

$$81+x^{2}=144$$

Subtract 81 from both sides.

$$x^{2}=144-81$$

Subtract 81 from 144 to get 63.

$$x^{2}=63$$

Take the square root of both sides of the equation.

$$x=3\sqrt{7} x=-3\sqrt{7}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$81+x^{2}=12^{2}$$

Calculate 12 to the power of 2 and get 144.

$$81+x^{2}=144$$

Subtract 144 from both sides.

$$81+x^{2}-144=0$$

Subtract 144 from 81 to get -63.

$$-63+x^{2}=0$$

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.

$$x^{2}-63=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -63 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-63\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-63\right)}}{2}$$

Multiply -4 times -63.

$$x=\frac{0±\sqrt{252}}{2}$$

Take the square root of 252.

$$x=\frac{0±6\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{7}}{2} when ± is plus.

$$x=3\sqrt{7}$$

Now solve the equation x=\frac{0±6\sqrt{7}}{2} when ± is minus.

$$x=-3\sqrt{7}$$

The equation is now solved.

$$x=3\sqrt{7} x=-3\sqrt{7}$$