Solve 2x^2/9-1/50=0

$$\frac { 2 x ^ { 2 } } { 9 } - \frac { 1 } { 50 } = 0$$

Solve for x

$$x=\frac{3}{10}=0.3$$

$$x=-\frac{3}{10}=-0.3$$

Steps Using Difference of Squares

Multiply both sides of the equation by 450, the least common multiple of 9,50.

$$50\times 2x^{2}-9=0$$

Multiply 50 and 2 to get 100.

$$100x^{2}-9=0$$

Consider 100x^{2}-9. Rewrite 100x^{2}-9 as \left(10x\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(10x-3\right)\left(10x+3\right)=0$$

To find equation solutions, solve 10x-3=0 and 10x+3=0.

$$x=\frac{3}{10} x=-\frac{3}{10}$$

Steps by Finding Square Root

Multiply both sides of the equation by 450, the least common multiple of 9,50.

$$50\times 2x^{2}-9=0$$

Multiply 50 and 2 to get 100.

$$100x^{2}-9=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$100x^{2}=9$$

Divide both sides by 100.

$$x^{2}=\frac{9}{100}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{10} x=-\frac{3}{10}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 450, the least common multiple of 9,50.

$$50\times 2x^{2}-9=0$$

Multiply 50 and 2 to get 100.

$$100x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 100\left(-9\right)}}{2\times 100}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 100\left(-9\right)}}{2\times 100}$$

Multiply -4 times 100.

$$x=\frac{0±\sqrt{-400\left(-9\right)}}{2\times 100}$$

Multiply -400 times -9.

$$x=\frac{0±\sqrt{3600}}{2\times 100}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\times 100}$$

Multiply 2 times 100.

$$x=\frac{0±60}{200}$$

Now solve the equation x=\frac{0±60}{200} when ± is plus. Reduce the fraction \frac{60}{200} to lowest terms by extracting and canceling out 20.

$$x=\frac{3}{10}$$

Now solve the equation x=\frac{0±60}{200} when ± is minus. Reduce the fraction \frac{-60}{200} to lowest terms by extracting and canceling out 20.

$$x=-\frac{3}{10}$$

The equation is now solved.

$$x=\frac{3}{10} x=-\frac{3}{10}$$