Solve x^2=217.98^2+269.88^2

$${ x }^{ 2 } = { 217.98 }^{ 2 } + { 269.88 }^{ 2 }$$

Solve for x

$$x = \frac{519 \sqrt{1117}}{50} \approx 346.915688316$$

$$x = -\frac{519 \sqrt{1117}}{50} \approx -346.915688316$$

Steps by Finding Square Root

Calculate 217.98 to the power of 2 and get 47515.2804.

$$x^{2}=47515.2804+269.88^{2}$$

Calculate 269.88 to the power of 2 and get 72835.2144.

$$x^{2}=47515.2804+72835.2144$$

Add 47515.2804 and 72835.2144 to get 120350.4948.

$$x^{2}=120350.4948$$

Take the square root of both sides of the equation.

$$x=\frac{519\sqrt{1117}}{50} x=-\frac{519\sqrt{1117}}{50}$$

Steps Using the Quadratic Formula

Calculate 217.98 to the power of 2 and get 47515.2804.

$$x^{2}=47515.2804+269.88^{2}$$

Calculate 269.88 to the power of 2 and get 72835.2144.

$$x^{2}=47515.2804+72835.2144$$

Add 47515.2804 and 72835.2144 to get 120350.4948.

$$x^{2}=120350.4948$$

Subtract 120350.4948 from both sides.

$$x^{2}-120350.4948=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -120350.4948 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-120350.4948\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-120350.4948\right)}}{2}$$

Multiply -4 times -120350.4948.

$$x=\frac{0±\sqrt{481401.9792}}{2}$$

Take the square root of 481401.9792.

$$x=\frac{0±\frac{519\sqrt{1117}}{25}}{2}$$

Now solve the equation x=\frac{0±\frac{519\sqrt{1117}}{25}}{2} when ± is plus.

$$x=\frac{519\sqrt{1117}}{50}$$

Now solve the equation x=\frac{0±\frac{519\sqrt{1117}}{25}}{2} when ± is minus.

$$x=-\frac{519\sqrt{1117}}{50}$$

The equation is now solved.

$$x=\frac{519\sqrt{1117}}{50} x=-\frac{519\sqrt{1117}}{50}$$