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Solve the equation by factoring: x2 - 5x - 14 a. X = -2 or 7 b. X = 2 and - 7 c. x = -2 or -7 d. X = 2 or 7

User Roydukkey
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We need to solve the quadratic equation:

x^2 - 5 x - 14 = 0 by factoring.

So we look for a pair of factors whose product is -14 and when combined render - 5. So we find the pair "-7 and 2"

Their product = (-7) * 2 = -14

combining them we get: -7 + 2 = -5

So we used them to split the middle term in the equation:

x^2 - 5 x - 14 = 0

x^2 - 7 x + 2 x - 14 = 0

Factor by grouping:

x ( x - 7) + 2 x - 14 = 0

x (x - 7) + 2 (x - 7) = 0

(x - 7) (x + 2 ) = 0

Then for this product to render zero, (x - 7) must be zero (so x = 7)

or (x + 2) is zero (and therefore x = -2)

Then we look for the answers x = -2 or x = 7

This coincides with answer (a) in your list.

User Lilya
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