Solve 15^2+19.639^2=x^2

$${ 15 }^{ 2 } + { 19.639 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{610690321}}{1000} \approx 24.712149259$$

$$x = -\frac{\sqrt{610690321}}{1000} \approx -24.712149259$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$225+19.639^{2}=x^{2}$$

Calculate 19.639 to the power of 2 and get 385.690321.

$$225+385.690321=x^{2}$$

Add 225 and 385.690321 to get 610.690321.

$$610.690321=x^{2}$$

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

$$x^{2}=610.690321$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{610690321}}{1000} x=-\frac{\sqrt{610690321}}{1000}$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$225+19.639^{2}=x^{2}$$

Calculate 19.639 to the power of 2 and get 385.690321.

$$225+385.690321=x^{2}$$

Add 225 and 385.690321 to get 610.690321.

$$610.690321=x^{2}$$

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

$$x^{2}=610.690321$$

Subtract 610.690321 from both sides.

$$x^{2}-610.690321=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -610.690321 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-610.690321\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-610.690321\right)}}{2}$$

Multiply -4 times -610.690321.

$$x=\frac{0±\sqrt{2442.761284}}{2}$$

Take the square root of 2442.761284.

$$x=\frac{0±\frac{\sqrt{610690321}}{500}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{610690321}}{500}}{2} when ± is plus.

$$x=\frac{\sqrt{610690321}}{1000}$$

Now solve the equation x=\frac{0±\frac{\sqrt{610690321}}{500}}{2} when ± is minus.

$$x=-\frac{\sqrt{610690321}}{1000}$$

The equation is now solved.

$$x=\frac{\sqrt{610690321}}{1000} x=-\frac{\sqrt{610690321}}{1000}$$