Precalculus Examples

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

Step 1

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

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

Step 2

Add $16$ to both sides of the equation.

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

Step 3

Factor using the perfect square rule.

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Step 3.1

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

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

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.

$8 x = 2 \cdot x \cdot 4$

Step 3.3

Rewrite the polynomial.

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

Step 3.4

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

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

Step 4

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

$x - 4 = 0$

Step 5

Add $4$ to both sides of the equation.

$x = 4$

Step 6