Pre-Algebra Examples

$r (r - 14) = - 49$

Step 1

Simplify $r (r - 14)$ .

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Step 1.1

Apply the distributive property.

$r \cdot r + r \cdot - 14 = - 49$

Step 1.2

Simplify the expression.

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Step 1.2.1

Multiply $r$ by $r$ .

$r^{2} + r \cdot - 14 = - 49$

Step 1.2.2

Move $- 14$ to the left of $r$ .

$r^{2} - 14 r = - 49$

Step 2

Add $49$ to both sides of the equation.

$r^{2} - 14 r + 49 = 0$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $49$ as $7^{2}$ .

$r^{2} - 14 r + 7^{2} = 0$

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.

$14 r = 2 \cdot r \cdot 7$

Step 3.3

Rewrite the polynomial.

$r^{2} - 2 \cdot r \cdot 7 + 7^{2} = 0$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = r$ and $b = 7$ .

${(r - 7)}^{2} = 0$

Step 4

Set the $r - 7$ equal to $0$ .

$r - 7 = 0$

Step 5

Add $7$ to both sides of the equation.

$r = 7$