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Question what-a

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

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$6 x squared, plus 5 x, minus 7, equals 0$

What are the solutions to the given equation?

A.

$the fraction with numerator negative 5, plus or minus the square root of 25 plus 168, end root, and denominator 12$

B.

$the fraction with numerator negative 6, plus or minus the square root of 25 plus 168, end root, and denominator 12$

C.

$the fraction with numerator negative 5, plus or minus the square root of 36 minus 168, end root, and denominator 12$

D.

$the fraction with numerator negative 6, plus or minus the square root of 36 minus 168, end root, and denominator 12$

What are the solutions 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. The quadratic formula, $x equals, the fraction with numerator negative b plus or minus, the square root of, b squared, minus 4 a, c, end root, and denominator 2 a, end fraction$ , can be used to find the solutions to an equation in the form $a, x squared, plus b x, plus c, equals 0$ . In the given equation, $a, equals 6$ , $b equals 5$ , and $c equals negative 7$ . Substituting these values into the quadratic formula gives $the fraction with numerator negative 5 plus or minus, the square root of, 5 squared minus 4, times 6, times 7, end root, and denominator 2 times 6, end fraction$ , or $the fraction with numerator negative 5 plus or minus, the square root of, 25 minus 168, end root, and denominator 12, end fraction$ .

Choice B is incorrect and may result from using $the fraction with numerator negative a, plus or minus, the square root of, b squared, minus 4 a, c, end root, and denominator 2 a, end fraction$ as the quadratic formula. Choice C is incorrect and may result from using $the fraction with numerator negative b plus or minus, the square root of, a, squared, plus 4 a, c, end root, and denominator 2 a, end fraction$ as the quadratic formula. Choice D is incorrect and may result from using $the fraction with numerator negative a, plus or minus, the square root of, a, squared, plus 4 a, c, end root, and denominator 2 a, end fraction$ as the quadratic formula.

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