Solve 100x^2-255=0

$$100 { x }^{ 2 } -255=0$$

Solve for x

$$x = \frac{\sqrt{255}}{10} \approx 1.596871942$$

$$x = -\frac{\sqrt{255}}{10} \approx -1.596871942$$

Steps by Finding Square Root

Add 255 to both sides. Anything plus zero gives itself.

$$100x^{2}=255$$

Divide both sides by 100.

$$x^{2}=\frac{255}{100}$$

Reduce the fraction \frac{255}{100} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{51}{20}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{255}}{10} x=-\frac{\sqrt{255}}{10}$$

Steps Using the Quadratic Formula

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.

$$100x^{2}-255=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -255 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 100\left(-255\right)}}{2\times 100}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 100\left(-255\right)}}{2\times 100}$$

Multiply -4 times 100.

$$x=\frac{0±\sqrt{-400\left(-255\right)}}{2\times 100}$$

Multiply -400 times -255.

$$x=\frac{0±\sqrt{102000}}{2\times 100}$$

Take the square root of 102000.

$$x=\frac{0±20\sqrt{255}}{2\times 100}$$

Multiply 2 times 100.

$$x=\frac{0±20\sqrt{255}}{200}$$

Now solve the equation x=\frac{0±20\sqrt{255}}{200} when ± is plus.

$$x=\frac{\sqrt{255}}{10}$$

Now solve the equation x=\frac{0±20\sqrt{255}}{200} when ± is minus.

$$x=-\frac{\sqrt{255}}{10}$$

The equation is now solved.

$$x=\frac{\sqrt{255}}{10} x=-\frac{\sqrt{255}}{10}$$