Algebra Examples

$16 x^{2} = 81$

Step 1

Subtract $81$ from both sides of the equation.

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

Step 2

Factor the left side.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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 $b = 9$ .

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