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How many root(s) does the following equation have? Explain how you know for credit.

-6x2 - 6x + 7 = 7

User Ppr
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1 Answer

5 votes

Answer:

This equation has two roots. We know this because of the format it is in. Any expression in the form ax² + bx + c is a quadratic one, which describes a parabola and has two roots.

In this case, the roots are -1 and 0.

Explanation:

Let's see if we can find those values:

-6x² - 6x + 7 = 7

-6x² - 6x = 0

x² + x = 0

x(x + 1) = 0

x = -1, 0

We could also run through solving this by completing the square:

-6x² - 6x + 7 = 7

-6x² - 6x = 0

x² + x = 0

x² + x + 0.25 = 0.25

(x + .5)² = 0.25

x + .5 = ±√0.25

x + .5 = ± 0.5

x = -0.5 ± 0.5

x = -1, 0

User Pavon
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