Question 595164
Let's start from the beginning. 
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I generally work these absolute value problems as two separate problems. I do this in two steps. First, I assign a plus sign to the entire quantity inside the absolute value signs and work that as one problem without using the absolute value signs. Second, I assign a minus sign to the entire quantity inside the absolute value signs and work that as a second problem without the absolute value signs.
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How does this system work for this problem?  Here we go ...
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The quantity inside the absolute value signs is (12x^2 - x - 2). Put a + sign in front of this quantity and it becomes just 12x^2 - x - 2. Now ignoring the absolute value signs of the original problem, the original problem is reduced to solving:
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12x^2 - x - 2 = 1
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Subtract 1 from both sides to get rid of the 1 on the right side and you get the standard quadratic form:
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12x^2 - x - 3 = 0
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The easiest way to solve for x in this equation is to use the quadratic formula which as you should know by now says that for the standard quadratic form:
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{{{ax^2 + bx + c = 0}}}
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the answers for x are given by the form:
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{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
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For this problem, a (the multiplier of the x^2 term is +12, b (the multiplier of the x term) is -1, and c (the constant term) is -3. I'll leave you with the job of substituting these three values into the equation for x, but when you do you should get as the answers for x:
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{{{x = (1+-sqrt(145))/24}}}
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which if you convert to decimals results in the two values for x being x = 0.543399774116 and x = -0.460066440783.
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That's half the answer to this problem. We got these two values for x by assigning a plus sign to the quantity inside the absolute value signs of the original problem.
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Next, let's assign a minus sign to the quantity inside the absolute value signs and go through a similar exercise. Begin with the minus sign assigned as follows:
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-(12x2 - x - 2)
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Ignore the absolute value signs and set this quantity equal to 1 as the original problem requires. This second equation becomes:
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-(12x2 - x - 2) = 1
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You can remove the parentheses on the left side by changing the signs of all the terms inside to get:
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- 12x^2 + x + 2 = 1
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Again, get rid of the + 1 on the right side by subtracting 1 from both sides to get the standard quadratic form of:
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- 12x^2 + x + 1 = 0
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Apply the quadratic formula as we did in the first part. This time a (the multiplier of the x-squared) is -12, b (the multiplier of the x) is +1, and c (the constant) is +1.
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Substituting these values into the form:
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{{{x = (-b +- sqrt(  b^2-4*a*c ))/(2*a) }}}
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results in the two values:
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{{{x = (-1 +- sqrt(  49 ))/(-24) }}}
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which, by taking the square root of 49, reduces to:
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{{{x = (-1 +- 7)/(-24) }}}
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When you work this out, you get the two answers for x as:
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{{{x = -1/4}}} and {{{x = 1/3}}}
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So, in summary, for this problem we end up with four answers for x as follows:  
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x = 0.543399774116,  -0.460066440783, -1/4, and 1/3
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I hope this process of working the problem as two different problems, one with a plus sign preceding the entire quantity inside the absolute value signs, and one with a minus sign preceding the entire quantity inside the absolute value signs, is something that you can use to help you get through such problems. I found that it helped me to eliminate some confusion with such problems, and it works because it's just a way of applying the basic definition for absolute value.