Solve 15^2+19639^2=x^2

$${ 15 }^{ 2 } + { 19639 }^{ 2 } = { x }^{ 2 }$$

Solve for x

$$x=\sqrt{385690546}\approx 19639.005728397$$

$$x=-\sqrt{385690546}\approx -19639.005728397$$

Steps by Finding Square Root

Calculate 15 to the power of 2 and get 225.

$$225+19639^{2}=x^{2}$$

Calculate 19639 to the power of 2 and get 385690321.

$$225+385690321=x^{2}$$

Add 225 and 385690321 to get 385690546.

$$385690546=x^{2}$$

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

$$x^{2}=385690546$$

Take the square root of both sides of the equation.

$$x=\sqrt{385690546} x=-\sqrt{385690546}$$

Steps Using the Quadratic Formula

Calculate 15 to the power of 2 and get 225.

$$225+19639^{2}=x^{2}$$

Calculate 19639 to the power of 2 and get 385690321.

$$225+385690321=x^{2}$$

Add 225 and 385690321 to get 385690546.

$$385690546=x^{2}$$

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

$$x^{2}=385690546$$

Subtract 385690546 from both sides.

$$x^{2}-385690546=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -385690546 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-385690546\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-385690546\right)}}{2}$$

Multiply -4 times -385690546.

$$x=\frac{0±\sqrt{1542762184}}{2}$$

Take the square root of 1542762184.

$$x=\frac{0±2\sqrt{385690546}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{385690546}}{2} when ± is plus.

$$x=\sqrt{385690546}$$

Now solve the equation x=\frac{0±2\sqrt{385690546}}{2} when ± is minus.

$$x=-\sqrt{385690546}$$

The equation is now solved.

$$x=\sqrt{385690546} x=-\sqrt{385690546}$$