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# Algebra

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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 22, 2022

#1
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First we must simplify this equation.

We subtract (14x + 9) from both sides of the equation to get the quadratic $$ax^2 + 6x - 2$$ = 0

Then we apply the quadratic formula $$-b {+\over} \sqrt{b^2 - 4ac}\over2a$$ where a is the coefficient of x^2, b is the coefficient of x, and c is the constant.

Plugging it in, we get -3 + or - $$\sqrt{11}$$, the nonzero constant (for which 'a' has one solution) will most likely be the positive solution.

$$a = \sqrt{11} - 3$$

Jan 23, 2022