Solve the quadratic equation and substitute {ACT}

What is the value of (x + 2)(x - 3) + 5, when x² - x - 6 = - 4 ?
A.)  -2
B.)  -1
C.)  1
D.)  2
E.)  3

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Solve the equation x² - x - 6 = - 4, for x, and then substitute the value(s) into (x + 2)(x - 3) + 5

x² - x - 6 = - 4
x² - x - 2 = 0   {added 4 to each side}
(x - 2)(x + 1) = 0   {factored into two binomials}
x - 2 = 0   or   x + 1 = 0   {set each factor equal to 0}
x = 2   or   x = -1   {added 2 in first equation and subtracted 1 in second equation}

Beginning to get worried because you just got 2 solutions for x,
and the answer choices only show 1 number??  Read on!

(x + 2)(x - 3) + 5
= (2 + 2)(2 - 3) + 5   {substituted 2 in for x}
= 4(-1) + 5   {worked inside parentheses}
= - 4 + 5   {multiplied}
= 1   {added}

(x + 2)(x - 3) + 5
= (-1 + 2)(-1 - 3) + 5   {substituted -1 in for x}
= 1(-4) + 5   {worked inside parentheses}
= -4 + 5   {multiplied}
= 1   {added}

C.)  1


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