Solving a Quadratic and Evaluating an Expression

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, then substitute the value of x 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 and subtracted 1 from each side}

If x = 2:
(x + 2)(x - 3) + 5   {given expression}
=  (2 + 2)(2 - 3) + 5   {substituted 2 for x}
=  4(-1) + 5   {added inside parentheses}
=  -4 + 5   {multiplied}
= 1   {added}

If x = -1:
(x + 2)(x - 3) + 5   {given expression}
=  (-1 + 2)(-1 - 3) = 5   {substituted -1 for x}
=  1(-4) + 5   {added inside parentheses}
=  -4 + 5   {multiplied}
=  1   {added}

C.)  1

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