Solve 10^2+x^2=30^2

$$10 ^ { 2 } + x ^ { 2 } = 30 ^ { 2 }$$

Solve for x

$$x=20\sqrt{2}\approx 28.284271247$$

$$x=-20\sqrt{2}\approx -28.284271247$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$100+x^{2}=30^{2}$$

Calculate 30 to the power of 2 and get 900.

$$100+x^{2}=900$$

Subtract 100 from both sides.

$$x^{2}=900-100$$

Subtract 100 from 900 to get 800.

$$x^{2}=800$$

Take the square root of both sides of the equation.

$$x=20\sqrt{2} x=-20\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$100+x^{2}=30^{2}$$

Calculate 30 to the power of 2 and get 900.

$$100+x^{2}=900$$

Subtract 900 from both sides.

$$100+x^{2}-900=0$$

Subtract 900 from 100 to get -800.

$$-800+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-800=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -800 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-800\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-800\right)}}{2}$$

Multiply -4 times -800.

$$x=\frac{0±\sqrt{3200}}{2}$$

Take the square root of 3200.

$$x=\frac{0±40\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±40\sqrt{2}}{2} when ± is plus.

$$x=20\sqrt{2}$$

Now solve the equation x=\frac{0±40\sqrt{2}}{2} when ± is minus.

$$x=-20\sqrt{2}$$

The equation is now solved.

$$x=20\sqrt{2} x=-20\sqrt{2}$$