Solve by Factoring 16x^2=81

$16 x^{2} = 81$

Step 1

Subtract $81$ from both sides of the equation.

$16 x^{2} - 81 = 0$

Step 2

Rewrite $16 x^{2}$ as ${(4 x)}^{2}$ .

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

Step 3

Rewrite $81$ as $9^{2}$ .

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

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 x$ and $b = 9$ .

$(4 x + 9) (4 x - 9) = 0$

Step 5

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

$4 x + 9 = 0$

$4 x - 9 = 0$

Step 6

Set $4 x + 9$ equal to $0$ and solve for $x$ .

Set $4 x + 9$ equal to $0$ .

$4 x + 9 = 0$

Solve $4 x + 9 = 0$ for $x$ .

Subtract $9$ from both sides of the equation.

$4 x = - 9$

Divide each term in $4 x = - 9$ by $4$ and simplify.

Divide each term in $4 x = - 9$ by $4$ .

$\frac{4 x}{4} = \frac{- 9}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 9}{4}$

Divide $x$ by $1$ .

$x = \frac{- 9}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{9}{4}$

Step 7

Set $4 x - 9$ equal to $0$ and solve for $x$ .

Set $4 x - 9$ equal to $0$ .

$4 x - 9 = 0$

Solve $4 x - 9 = 0$ for $x$ .

Add $9$ to both sides of the equation.

$4 x = 9$

Divide each term in $4 x = 9$ by $4$ and simplify.

Divide each term in $4 x = 9$ by $4$ .

$\frac{4 x}{4} = \frac{9}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{9}{4}$

Divide $x$ by $1$ .

$x = \frac{9}{4}$

Step 8

The final solution is all the values that make $(4 x + 9) (4 x - 9) = 0$ true.

$x = - \frac{9}{4}, \frac{9}{4}$

Solve by Factoring 16x^2=81

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