Question

question 4 (mandatory) (1 point) saved
identify the values of a, b, and c you would use to substitute into the quadratic formula to solve $14x + 20x^2 = 17x - 25$.

a) $a = 20$; $b = -3$; $c = 25$
b) $a = 20$; $b = 31$; $c = -25$
c) $a = -20$; $b = -3$; $c = -25$
d) $a = -3$; $b = 20$; $c = 25$

Explanation:

Step1: Rearrange the equation

First, we need to rewrite the given equation \(14x + 20x^2 = 17x - 25\) in the standard quadratic form \(ax^2 + bx + c = 0\).

Subtract \(17x\) from both sides and add \(25\) to both sides:

\(20x^2 + 14x - 17x + 25 = 0\)

Step2: Simplify the equation

Simplify the like terms (\(14x - 17x\)):

\(20x^2 - 3x + 25 = 0\)

In the standard quadratic form \(ax^2 + bx + c = 0\), we can identify:

• \(a = 20\) (coefficient of \(x^2\))
• \(b = -3\) (coefficient of \(x\))
• \(c = 25\) (constant term)

Answer:

a) \(a = 20\); \(b = -3\); \(c = 25\)