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

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

Solve for x

$$x=\sqrt{337}\approx 18.357559751$$

$$x=-\sqrt{337}\approx -18.357559751$$

Steps by Finding Square Root

Calculate 9 to the power of 2 and get 81.

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

Calculate 16 to the power of 2 and get 256.

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

Add 81 and 256 to get 337.

$$337=x^{2}$$

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

$$x^{2}=337$$

Take the square root of both sides of the equation.

$$x=\sqrt{337} x=-\sqrt{337}$$

Steps Using the Quadratic Formula

Calculate 9 to the power of 2 and get 81.

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

Calculate 16 to the power of 2 and get 256.

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

Add 81 and 256 to get 337.

$$337=x^{2}$$

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

$$x^{2}=337$$

Subtract 337 from both sides.

$$x^{2}-337=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -337 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-337\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-337\right)}}{2}$$

Multiply -4 times -337.

$$x=\frac{0±\sqrt{1348}}{2}$$

Take the square root of 1348.

$$x=\frac{0±2\sqrt{337}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{337}}{2} when ± is plus.

$$x=\sqrt{337}$$

Now solve the equation x=\frac{0±2\sqrt{337}}{2} when ± is minus.

$$x=-\sqrt{337}$$

The equation is now solved.

$$x=\sqrt{337} x=-\sqrt{337}$$