Math CentralQuandaries & Queries


Question from Bj, a student:

Solve for x: 5x^2 - 35x = 0

Bj, start by factoring:

5x² - 35x = 0
5x(x - 7) = 0

The reason we factor things equal to zero is because the only way to get zero when multiplying two numbers is if one or the other (or both) factors are zero. That means one or the other (or both) of the following equations is correct:

5x = 0 or x - 7 = 0

You see, these are the two quantities that are the factors making 0, so we break the equation 5x(x - 7) = 0 into two separate simpler equations: 5x = 0 and x - 7 = 0.

Solve each of these equations separately for x. The results are the value(s) of x you can use in the original equation 5x² - 35x = 0 that work.

Hope this helps,
Stephen La Rocque.

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