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2.2 Nonlinear Equations in One Variable - Quadratic solving (factoring, quadratic formula, completing square)
0:00

open parenthesis, x plus 2, close parenthesis, times, open parenthesis, x plus 3, close parenthesis, equals, open parenthesis, x minus 2, close parenthesis, times, open parenthesis, x minus 3, close parenthesis, plus 10

Which of the following is a solution to the given equation?

A.

1

B.

0

C.

negative 2

D.

negative 5

Which of the following is a solution to the given equation?

Hard-difficulty · SAT Math · Nonlinear Equations in One Variable — Quadratic solving (factoring, quadratic formula, completing square). Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice A is correct. Applying the distributive property on the left- and right-hand sides of the given equation yields x squared, plus 2 x, plus 3 x, plus 6, equals, x squared, minus 2 x, minus 3 x, plus 6, plus 10, or x squared, plus 5 x, plus 6, equals, x squared, minus 5 x, plus 16. Subtracting x squared from and adding 5 x to both sides of this equation yields 10 x plus 6, equals 16. Subtracting 6 from both sides of this equation and then dividing both sides by 10 yields x equals 1.

Choices B, C, and D are incorrect. Substituting 0, negative 2, or negative 5 for x in the given equation will result in a false statement. If x equals 0, the given equation becomes 6 equals 16; if x equals negative 2, the given equation becomes 0 equals 30; and if x equals negative 5, the given equation becomes 6 equals 66. Therefore, the values 0, negative 2, and negative 5 aren’t solutions to the given equation.

 

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