Solve 2900x^2=3509

$$2900 x ^ { 2 } = 3509$$

Solve for x

$$x = \frac{11}{10} = 1\frac{1}{10} = 1.1$$

$$x = -\frac{11}{10} = -1\frac{1}{10} = -1.1$$

Steps Using Difference of Squares

Divide both sides by 2900.

$$x^{2}=\frac{3509}{2900}$$

Reduce the fraction \frac{3509}{2900} to lowest terms by extracting and canceling out 29.

$$x^{2}=\frac{121}{100}$$

Subtract \frac{121}{100} from both sides.

$$x^{2}-\frac{121}{100}=0$$

Multiply both sides by 100.

$$100x^{2}-121=0$$

Consider 100x^{2}-121. Rewrite 100x^{2}-121 as \left(10x\right)^{2}-11^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(10x-11\right)\left(10x+11\right)=0$$

To find equation solutions, solve 10x-11=0 and 10x+11=0.

$$x=\frac{11}{10} x=-\frac{11}{10}$$

Steps by Finding Square Root

Divide both sides by 2900.

$$x^{2}=\frac{3509}{2900}$$

Reduce the fraction \frac{3509}{2900} to lowest terms by extracting and canceling out 29.

$$x^{2}=\frac{121}{100}$$

Take the square root of both sides of the equation.

$$x=\frac{11}{10} x=-\frac{11}{10}$$

Steps Using the Quadratic Formula

Divide both sides by 2900.

$$x^{2}=\frac{3509}{2900}$$

Reduce the fraction \frac{3509}{2900} to lowest terms by extracting and canceling out 29.

$$x^{2}=\frac{121}{100}$$

Subtract \frac{121}{100} from both sides.

$$x^{2}-\frac{121}{100}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{121}{100} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{121}{100}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{121}{100}\right)}}{2}$$

Multiply -4 times -\frac{121}{100}.

$$x=\frac{0±\sqrt{\frac{121}{25}}}{2}$$

Take the square root of \frac{121}{25}.

$$x=\frac{0±\frac{11}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{11}{5}}{2} when ± is plus.

$$x=\frac{11}{10}$$

Now solve the equation x=\frac{0±\frac{11}{5}}{2} when ± is minus.

$$x=-\frac{11}{10}$$

The equation is now solved.

$$x=\frac{11}{10} x=-\frac{11}{10}$$