Solve 25-100x^2=0

$$25-100 { x }^{ 2 } =0$$

Solve for x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Steps by Finding Square Root

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$-100x^{2}=-25$$

Divide both sides by -100.

$$x^{2}=\frac{-25}{-100}$$

Reduce the fraction \frac{-25}{-100} to lowest terms by extracting and canceling out -25.

$$x^{2}=\frac{1}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{2} x=-\frac{1}{2}$$

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.

$$-100x^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -100 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-100\right)\times 25}}{2\left(-100\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-100\right)\times 25}}{2\left(-100\right)}$$

Multiply -4 times -100.

$$x=\frac{0±\sqrt{400\times 25}}{2\left(-100\right)}$$

Multiply 400 times 25.

$$x=\frac{0±\sqrt{10000}}{2\left(-100\right)}$$

Take the square root of 10000.

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

Multiply 2 times -100.

$$x=\frac{0±100}{-200}$$

Now solve the equation x=\frac{0±100}{-200} when ± is plus. Reduce the fraction \frac{100}{-200} to lowest terms by extracting and canceling out 100.

$$x=-\frac{1}{2}$$

Now solve the equation x=\frac{0±100}{-200} when ± is minus. Reduce the fraction \frac{-100}{-200} to lowest terms by extracting and canceling out 100.

$$x=\frac{1}{2}$$

The equation is now solved.

$$x=-\frac{1}{2} x=\frac{1}{2}$$