Finite Math Examples

$2 r^{2} - 8 r + 8 = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Factor $2$ out of $2 r^{2} - 8 r + 8$ .

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Step 1.1.1

Factor $2$ out of $2 r^{2}$ .

$2 (r^{2}) - 8 r + 8 = 0$

Step 1.1.2

Factor $2$ out of $- 8 r$ .

$2 (r^{2}) + 2 (- 4 r) + 8 = 0$

Step 1.1.3

Factor $2$ out of $8$ .

$2 r^{2} + 2 (- 4 r) + 2 \cdot 4 = 0$

Step 1.1.4

Factor $2$ out of $2 r^{2} + 2 (- 4 r)$ .

$2 (r^{2} - 4 r) + 2 \cdot 4 = 0$

Step 1.1.5

Factor $2$ out of $2 (r^{2} - 4 r) + 2 \cdot 4$ .

$2 (r^{2} - 4 r + 4) = 0$

Step 1.2

Factor using the perfect square rule.

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Step 1.2.1

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

$2 (r^{2} - 4 r + 2^{2}) = 0$

Step 1.2.2

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

$4 r = 2 \cdot r \cdot 2$

Step 1.2.3

Rewrite the polynomial.

$2 (r^{2} - 2 \cdot r \cdot 2 + 2^{2}) = 0$

Step 1.2.4

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

$2 {(r - 2)}^{2} = 0$

Step 2

Divide each term in $2 {(r - 2)}^{2} = 0$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 {(r - 2)}^{2} = 0$ by $2$ .

$\frac{2 {(r - 2)}^{2}}{2} = \frac{0}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 {(r - 2)}^{2}}{2} = \frac{0}{2}$

Step 2.2.1.2

Divide ${(r - 2)}^{2}$ by $1$ .

${(r - 2)}^{2} = \frac{0}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $0$ by $2$ .

${(r - 2)}^{2} = 0$

Step 3

Set the $r - 2$ equal to $0$ .

$r - 2 = 0$

Step 4

Add $2$ to both sides of the equation.

$r = 2$

Step 5