Pre-Algebra Examples

$w^{2} + 16 = 8 w$

Step 1

Subtract $8 w$ from both sides of the equation.

$w^{2} + 16 - 8 w = 0$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rearrange terms.

$w^{2} - 8 w + 16 = 0$

Step 2.2

Rewrite $16$ as $4^{2}$ .

$w^{2} - 8 w + 4^{2} = 0$

Step 2.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 w = 2 \cdot w \cdot 4$

Step 2.4

Rewrite the polynomial.

$w^{2} - 2 \cdot w \cdot 4 + 4^{2} = 0$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = w$ and $b = 4$ .

${(w - 4)}^{2} = 0$

Step 3

Set the $w - 4$ equal to $0$ .

$w - 4 = 0$

Step 4

Add $4$ to both sides of the equation.

$w = 4$