Answer: B. x = -7
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Explanation:
There are at least two ways to do this. Method 1 is to FOIL out the left hand side, then subtract 18 from both sides, and apply the quadratic formula or factor
(x-2)(x+5) = 18
x^2+5x-2x-10 = 18
x^2+3x-10 = 18
x^2+3x-10-18 = 0
x^2+3x-28 = 0
(x+7)(x-4) = 0
x+7 = 0 or x-4 = 0
x = -7 or x = 4
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Method 2 is to go through each answer choice and plug those x values, one at a time, into the original equation. If you get the same number on both sides, then you found your answer.
So for instance, x = -10 does not work because
(x-2)*(x+5) = 18
(-10-2)*(-10+5) = 18 ... replace every x with -10
(-12)*(-5) = 18
60 = 18 .... this equation is false, so x = -10 is not a solution
But x = -7 works as method 1 shows above, and we can confirm it as such
(x-2)*(x+5) = 18
(-7-2)*(-7+5) = 18 ... x is replaced with -7
(-9)*(-2) = 18
18 = 18 ..... true equation; confirms x = -7
You should find that choices C and D are similar to choice A, and they won't work.
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For the sake of completeness, let's confirm x = 4 as well
(x-2)*(x+5) = 18
(4-2)*(4+5) = 18
(2)*(9) = 18
18 = 18
Both solutions found in method 1 have been confirmed.
