Solve x^2+left(19div2right)^2=20^2

$${ x }^{ 2 } + { \left(19 \div 2 \right) }^{ 2 } = { 20 }^{ 2 }$$

Solve for x

$$x = \frac{\sqrt{1239}}{2} \approx 17.599715907$$

$$x = -\frac{\sqrt{1239}}{2} \approx -17.599715907$$

Steps by Finding Square Root

Calculate \frac{19}{2} to the power of 2 and get \frac{361}{4}.

$$x^{2}+\frac{361}{4}=20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}+\frac{361}{4}=400$$

Subtract \frac{361}{4} from both sides.

$$x^{2}=400-\frac{361}{4}$$

Subtract \frac{361}{4} from 400 to get \frac{1239}{4}.

$$x^{2}=\frac{1239}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{1239}}{2} x=-\frac{\sqrt{1239}}{2}$$

Steps Using the Quadratic Formula

Calculate \frac{19}{2} to the power of 2 and get \frac{361}{4}.

$$x^{2}+\frac{361}{4}=20^{2}$$

Calculate 20 to the power of 2 and get 400.

$$x^{2}+\frac{361}{4}=400$$

Subtract 400 from both sides.

$$x^{2}+\frac{361}{4}-400=0$$

Subtract 400 from \frac{361}{4} to get -\frac{1239}{4}.

$$x^{2}-\frac{1239}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1239}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1239}{4}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1239}{4}\right)}}{2}$$

Multiply -4 times -\frac{1239}{4}.

$$x=\frac{0±\sqrt{1239}}{2}$$

Now solve the equation x=\frac{0±\sqrt{1239}}{2} when ± is plus.

$$x=\frac{\sqrt{1239}}{2}$$

Now solve the equation x=\frac{0±\sqrt{1239}}{2} when ± is minus.

$$x=-\frac{\sqrt{1239}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{1239}}{2} x=-\frac{\sqrt{1239}}{2}$$