Solve 2.5=x^2*1000

$$2.5 = x ^ { 2 } \cdot 1000$$

Solve for x

$$x=0.05$$

$$x=-0.05$$

Steps Using Difference of Squares

Divide both sides by 1000.

$$\frac{2.5}{1000}=x^{2}$$

Expand \frac{2.5}{1000} by multiplying both numerator and the denominator by 10.

$$\frac{25}{10000}=x^{2}$$

Reduce the fraction \frac{25}{10000} to lowest terms by extracting and canceling out 25.

$$\frac{1}{400}=x^{2}$$

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

$$x^{2}=\frac{1}{400}$$

Subtract \frac{1}{400} from both sides.

$$x^{2}-\frac{1}{400}=0$$

Multiply both sides by 400.

$$400x^{2}-1=0$$

Consider 400x^{2}-1. Rewrite 400x^{2}-1 as \left(20x\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(20x-1\right)\left(20x+1\right)=0$$

To find equation solutions, solve 20x-1=0 and 20x+1=0.

$$x=\frac{1}{20} x=-\frac{1}{20}$$

Steps by Finding Square Root

Divide both sides by 1000.

$$\frac{2.5}{1000}=x^{2}$$

Expand \frac{2.5}{1000} by multiplying both numerator and the denominator by 10.

$$\frac{25}{10000}=x^{2}$$

Reduce the fraction \frac{25}{10000} to lowest terms by extracting and canceling out 25.

$$\frac{1}{400}=x^{2}$$

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

$$x^{2}=\frac{1}{400}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{20} x=-\frac{1}{20}$$

Steps Using the Quadratic Formula

Divide both sides by 1000.

$$\frac{2.5}{1000}=x^{2}$$

Expand \frac{2.5}{1000} by multiplying both numerator and the denominator by 10.

$$\frac{25}{10000}=x^{2}$$

Reduce the fraction \frac{25}{10000} to lowest terms by extracting and canceling out 25.

$$\frac{1}{400}=x^{2}$$

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

$$x^{2}=\frac{1}{400}$$

Subtract \frac{1}{400} from both sides.

$$x^{2}-\frac{1}{400}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1}{400} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{400}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{400}\right)}}{2}$$

Multiply -4 times -\frac{1}{400}.

$$x=\frac{0±\sqrt{\frac{1}{100}}}{2}$$

Take the square root of \frac{1}{100}.

$$x=\frac{0±\frac{1}{10}}{2}$$

Now solve the equation x=\frac{0±\frac{1}{10}}{2} when ± is plus.

$$x=\frac{1}{20}$$

Now solve the equation x=\frac{0±\frac{1}{10}}{2} when ± is minus.

$$x=-\frac{1}{20}$$

The equation is now solved.

$$x=\frac{1}{20} x=-\frac{1}{20}$$