Solve 9^2+x^2=16^2

$$9 ^ { 2 } + x ^ { 2 } = 16 ^ { 2 }$$

Solve for x

$$x=5\sqrt{7}\approx 13.228756555$$

$$x=-5\sqrt{7}\approx -13.228756555$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

$$81+x^{2}=16^{2}$$

Calculate 16 to the power of 2 and get 256.

$$81+x^{2}=256$$

Subtract 81 from both sides.

$$x^{2}=256-81$$

Subtract 81 from 256 to get 175.

$$x^{2}=175$$

Take the square root of both sides of the equation.

$$x=5\sqrt{7} x=-5\sqrt{7}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

$$81+x^{2}=16^{2}$$

Calculate 16 to the power of 2 and get 256.

$$81+x^{2}=256$$

Subtract 256 from both sides.

$$81+x^{2}-256=0$$

Subtract 256 from 81 to get -175.

$$-175+x^{2}=0$$

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.

$$x^{2}-175=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -175 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-175\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-175\right)}}{2}$$

Multiply -4 times -175.

$$x=\frac{0±\sqrt{700}}{2}$$

Take the square root of 700.

$$x=\frac{0±10\sqrt{7}}{2}$$

Now solve the equation x=\frac{0±10\sqrt{7}}{2} when ± is plus.

$$x=5\sqrt{7}$$

Now solve the equation x=\frac{0±10\sqrt{7}}{2} when ± is minus.

$$x=-5\sqrt{7}$$

The equation is now solved.

$$x=5\sqrt{7} x=-5\sqrt{7}$$