Solve by Factoring w^2-2w=15

$w^{2} - 2 w = 15$

Move $15$ to the left side of the equation by subtracting it from both sides.

$w^{2} - 2 w - 15 = 0$

Factor $w^{2} - 2 w - 15$ using the AC method.

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Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 15$ and whose sum is $- 2$ .

$- 5, 3$

Write the factored form using these integers.

$(w - 5) (w + 3) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$w - 5 = 0$

$w + 3 = 0$

Set the first factor equal to $0$ and solve.

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Set the first factor equal to $0$ .

$w - 5 = 0$

Add $5$ to both sides of the equation.

$w = 5$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$w + 3 = 0$

Subtract $3$ from both sides of the equation.

$w = - 3$

The final solution is all the values that make $(w - 5) (w + 3) = 0$ true.

$w = 5, - 3$

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