Solve 243m^2-147=0

$$243 m ^ { 2 } - 147 = 0$$

Solve for m

$$m=\frac{7}{9}\approx 0.777777778$$

$$m=-\frac{7}{9}\approx -0.777777778$$

Steps Using Difference of Squares

Divide both sides by 3.

$$81m^{2}-49=0$$

Consider 81m^{2}-49. Rewrite 81m^{2}-49 as \left(9m\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9m-7\right)\left(9m+7\right)=0$$

To find equation solutions, solve 9m-7=0 and 9m+7=0.

$$m=\frac{7}{9} m=-\frac{7}{9}$$

Steps by Finding Square Root

Add 147 to both sides. Anything plus zero gives itself.

$$243m^{2}=147$$

Divide both sides by 243.

$$m^{2}=\frac{147}{243}$$

Reduce the fraction \frac{147}{243} to lowest terms by extracting and canceling out 3.

$$m^{2}=\frac{49}{81}$$

Take the square root of both sides of the equation.

$$m=\frac{7}{9} m=-\frac{7}{9}$$

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.

$$243m^{2}-147=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 243 for a, 0 for b, and -147 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 243\left(-147\right)}}{2\times 243}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 243\left(-147\right)}}{2\times 243}$$

Multiply -4 times 243.

$$m=\frac{0±\sqrt{-972\left(-147\right)}}{2\times 243}$$

Multiply -972 times -147.

$$m=\frac{0±\sqrt{142884}}{2\times 243}$$

Take the square root of 142884.

$$m=\frac{0±378}{2\times 243}$$

Multiply 2 times 243.

$$m=\frac{0±378}{486}$$

Now solve the equation m=\frac{0±378}{486} when ± is plus. Reduce the fraction \frac{378}{486} to lowest terms by extracting and canceling out 54.

$$m=\frac{7}{9}$$

Now solve the equation m=\frac{0±378}{486} when ± is minus. Reduce the fraction \frac{-378}{486} to lowest terms by extracting and canceling out 54.

$$m=-\frac{7}{9}$$

The equation is now solved.

$$m=\frac{7}{9} m=-\frac{7}{9}$$