Solve 545.8=500*1+500x^2

$$545.8=500 \times 1+500 { x }^{ 2 }$$

Solve for x

$$x=\frac{\sqrt{229}}{50}\approx 0.302654919$$

$$x=-\frac{\sqrt{229}}{50}\approx -0.302654919$$

Steps by Finding Square Root

Multiply 500 and 1 to get 500.

$$545.8=500+500x^{2}$$

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

$$500+500x^{2}=545.8$$

Subtract 500 from both sides.

$$500x^{2}=545.8-500$$

Subtract 500 from 545.8 to get 45.8.

$$500x^{2}=45.8$$

Divide both sides by 500.

$$x^{2}=\frac{45.8}{500}$$

Expand \frac{45.8}{500} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{458}{5000}$$

Reduce the fraction \frac{458}{5000} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{229}{2500}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{229}}{50} x=-\frac{\sqrt{229}}{50}$$

Steps Using the Quadratic Formula

Multiply 500 and 1 to get 500.

$$545.8=500+500x^{2}$$

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

$$500+500x^{2}=545.8$$

Subtract 545.8 from both sides.

$$500+500x^{2}-545.8=0$$

Subtract 545.8 from 500 to get -45.8.

$$-45.8+500x^{2}=0$$

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.

$$500x^{2}-45.8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 500 for a, 0 for b, and -45.8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 500\left(-45.8\right)}}{2\times 500}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 500\left(-45.8\right)}}{2\times 500}$$

Multiply -4 times 500.

$$x=\frac{0±\sqrt{-2000\left(-45.8\right)}}{2\times 500}$$

Multiply -2000 times -45.8.

$$x=\frac{0±\sqrt{91600}}{2\times 500}$$

Take the square root of 91600.

$$x=\frac{0±20\sqrt{229}}{2\times 500}$$

Multiply 2 times 500.

$$x=\frac{0±20\sqrt{229}}{1000}$$

Now solve the equation x=\frac{0±20\sqrt{229}}{1000} when ± is plus.

$$x=\frac{\sqrt{229}}{50}$$

Now solve the equation x=\frac{0±20\sqrt{229}}{1000} when ± is minus.

$$x=-\frac{\sqrt{229}}{50}$$

The equation is now solved.

$$x=\frac{\sqrt{229}}{50} x=-\frac{\sqrt{229}}{50}$$