Solve 8^2+18^2=x^2

$$8 ^ { 2 } + 18 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=2\sqrt{97}\approx 19.697715604$$

$$x=-2\sqrt{97}\approx -19.697715604$$

Steps by Finding Square Root

Calculate 8 to the power of 2 and get 64.

$$64+18^{2}=x^{2}$$

Calculate 18 to the power of 2 and get 324.

$$64+324=x^{2}$$

Add 64 and 324 to get 388.

$$388=x^{2}$$

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

$$x^{2}=388$$

Take the square root of both sides of the equation.

$$x=2\sqrt{97} x=-2\sqrt{97}$$

Steps Using the Quadratic Formula

Calculate 8 to the power of 2 and get 64.

$$64+18^{2}=x^{2}$$

Calculate 18 to the power of 2 and get 324.

$$64+324=x^{2}$$

Add 64 and 324 to get 388.

$$388=x^{2}$$

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

$$x^{2}=388$$

Subtract 388 from both sides.

$$x^{2}-388=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -388 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-388\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-388\right)}}{2}$$

Multiply -4 times -388.

$$x=\frac{0±\sqrt{1552}}{2}$$

Take the square root of 1552.

$$x=\frac{0±4\sqrt{97}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{97}}{2} when ± is plus.

$$x=2\sqrt{97}$$

Now solve the equation x=\frac{0±4\sqrt{97}}{2} when ± is minus.

$$x=-2\sqrt{97}$$

The equation is now solved.

$$x=2\sqrt{97} x=-2\sqrt{97}$$