Finite Math Examples

$64 + x^{2} = 16 x$

Step 1

Subtract $16 x$ from both sides of the equation.

$64 + x^{2} - 16 x = 0$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rearrange terms.

$64 - 16 x + x^{2} = 0$

Step 2.2

Rewrite $64$ as $8^{2}$ .

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

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.

$16 x = 2 \cdot 8 \cdot x$

Step 2.4

Rewrite the polynomial.

$8^{2} - 2 \cdot 8 \cdot x + x^{2} = 0$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 8$ and $b = x$ .

${(8 - x)}^{2} = 0$

Step 3

Set the $8 - x$ equal to $0$ .

$8 - x = 0$

Step 4

Solve for $x$ .

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Step 4.1

Subtract $8$ from both sides of the equation.

$- x = - 8$

Step 4.2

Divide each term in $- x = - 8$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- x = - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 8}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 8}{- 1}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 8$ by $- 1$ .

$x = 8$

Step 5