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Suppose that a is a nonzero constant for which the equation ax^2 + 20x + 7 = 14x + 9  has only one solution. Find this solution.

Jan 26, 2022

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ax^2 + 20x + 7 = 14x + 9             re-arrange

ax^2 + 6x -2 = 0          for only one solution ( one double root) the discriminant of the Quadratic Formula must = 0

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$$

b^2 - 4ac = 0

(6)^2 - 4 (a)(-2) = 0

8a = -36

a = -4.5

Jan 26, 2022