Pre-Algebra Examples

$s^{2} = 8 s - 16$

Step 1

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

$s^{2} - 8 s = - 16$

Step 2

Add $16$ to both sides of the equation.

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

Step 3

Factor using the perfect square rule.

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Step 3.1

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

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

Step 3.2

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

$8 s = 2 \cdot s \cdot 4$

Step 3.3

Rewrite the polynomial.

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

Step 3.4

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

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

Step 4

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

$s - 4 = 0$

Step 5

Add $4$ to both sides of the equation.

$s = 4$