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Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Medium

$5 x^{2} - 37 x - 24 = 0$

What is the positive solution to the given equation?

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Explanation

Choice C is correct. The left-hand side of the given equation can be factored as $(5 x + 3) (x - 8)$ . Therefore, the given equation, $5 x^{2} - 37 x - 24 = 0$ , can be written as $(5 x + 3) (x - 8) = 0$ . Applying the zero product property to this equation yields $5 x + 3 = 0$ and $x - 8 = 0$ . Subtracting $3$ from both sides of the equation $5 x + 3 = 0$ yields $5 x = - 3$ . Dividing both sides of this equation by $5$ yields $x = - \frac{3}{5}$ . Adding $8$ to both sides of the equation $x - 8 = 0$ yields $x equals 8$ . Therefore, the two solutions to the given equation, $5 x^{2} - 37 x - 24 = 0$ , are $- \frac{3}{5}$ and $8$ . It follows that $8$ is the positive solution to the given equation.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.