How many root(s) does the following equation have? Explain how you know for credit. -6x2 - 6x + 7 = 7

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.

Step-by-step 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

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.

the least common denominator is 40