# How do you solve #2x^2-2x-12=0#?

Divide the answer by two because every number in the equation is even.

Two and two are the factors of six that subtract to equal one.

If the multiplication result is zero, then zero must be one of the factors.

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Determine which factors in -6 add up to -1.

They are +2 and - 3.

The factors (x - 3) and (x + 2) may both equal zero.

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To solve the quadratic equation 2x^2 - 2x - 12 = 0, you can use the quadratic formula. First, identify the coefficients a, b, and c in the general quadratic equation form ax^2 + bx + c = 0. In this case, a = 2, b = -2, and c = -12. Then, substitute these values into the quadratic formula:

[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ]

Plugging in the values, we get:

[ x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(2)(-12)}}{2(2)} ]

Simplifying further:

[ x = \frac{2 \pm \sqrt{4 + 96}}{4} ] [ x = \frac{2 \pm \sqrt{100}}{4} ] [ x = \frac{2 \pm 10}{4} ]

So the solutions are:

[ x = \frac{2 + 10}{4} = \frac{12}{4} = 3 ] and [ x = \frac{2 - 10}{4} = \frac{-8}{4} = -2 ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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