Solve by Factoring 81x^2=4

$81 x^{2} = 4$

Step 1

Subtract $4$ from both sides of the equation.

$81 x^{2} - 4 = 0$

Step 2

Rewrite $81 x^{2}$ as ${(9 x)}^{2}$ .

${(9 x)}^{2} - 4 = 0$

Step 3

Rewrite $4$ as $2^{2}$ .

${(9 x)}^{2} - 2^{2} = 0$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 9 x$ and $b = 2$ .

$(9 x + 2) (9 x - 2) = 0$

Step 5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$9 x + 2 = 0$

$9 x - 2 = 0$

Step 6

Set $9 x + 2$ equal to $0$ and solve for $x$ .

Set $9 x + 2$ equal to $0$ .

$9 x + 2 = 0$

Solve $9 x + 2 = 0$ for $x$ .

Subtract $2$ from both sides of the equation.

$9 x = - 2$

Divide each term in $9 x = - 2$ by $9$ and simplify.

Divide each term in $9 x = - 2$ by $9$ .

$\frac{9 x}{9} = \frac{- 2}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 2}{9}$

Divide $x$ by $1$ .

$x = \frac{- 2}{9}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{9}$

Step 7

Set $9 x - 2$ equal to $0$ and solve for $x$ .

Set $9 x - 2$ equal to $0$ .

$9 x - 2 = 0$

Solve $9 x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$9 x = 2$

Divide each term in $9 x = 2$ by $9$ and simplify.

Divide each term in $9 x = 2$ by $9$ .

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

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 8

The final solution is all the values that make $(9 x + 2) (9 x - 2) = 0$ true.

$x = - \frac{2}{9}, \frac{2}{9}$

Solve by Factoring 81x^2=4

Related Questions

Support LCMGCF.com by disabling your adblocker.