Solve x^2=18^2+40^2

$$x ^ { 2 } = 18 ^ { 2 } + 40 ^ { 2 }$$

Solve for x

$$x=2\sqrt{481}\approx 43.863424399$$

$$x=-2\sqrt{481}\approx -43.863424399$$

Steps by Finding Square Root

Calculate 18 to the power of 2 and get 324.

$$x^{2}=324+40^{2}$$

Calculate 40 to the power of 2 and get 1600.

$$x^{2}=324+1600$$

Add 324 and 1600 to get 1924.

$$x^{2}=1924$$

Take the square root of both sides of the equation.

$$x=2\sqrt{481} x=-2\sqrt{481}$$

Steps Using the Quadratic Formula

Calculate 18 to the power of 2 and get 324.

$$x^{2}=324+40^{2}$$

Calculate 40 to the power of 2 and get 1600.

$$x^{2}=324+1600$$

Add 324 and 1600 to get 1924.

$$x^{2}=1924$$

Subtract 1924 from both sides.

$$x^{2}-1924=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1924 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1924\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1924\right)}}{2}$$

Multiply -4 times -1924.

$$x=\frac{0±\sqrt{7696}}{2}$$

Take the square root of 7696.

$$x=\frac{0±4\sqrt{481}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{481}}{2} when ± is plus.

$$x=2\sqrt{481}$$

Now solve the equation x=\frac{0±4\sqrt{481}}{2} when ± is minus.

$$x=-2\sqrt{481}$$

The equation is now solved.

$$x=2\sqrt{481} x=-2\sqrt{481}$$