SOLUTION: Please help me with this! 12x^2-5x-7, using completing the square. Thank you!

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Question 904911: Please help me with this!
12x^2-5x-7, using completing the square.
Thank you!
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: COMPLETING THE SQUARE solver for quadratics
Read this lesson on completing the square by prince_abubu, if you do not know how to complete the square.
Let's convert to standard form by dividing both sides by 12:
We have: . What we want to do now is to change this equation to a complete square . How can we find out values of somenumber and othernumber that would make it work?
Look at : . Since the coefficient in our equation that goes in front of x is -0.416666666666667, we know that -0.416666666666667=2*somenumber, or . So, we know that our equation can be rewritten as , and we do not yet know the other number.
We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that is equivalent to our original equation .


The highlighted red part must be equal to -0.583333333333333 (highlighted green part).

, or .
So, the equation converts to , or .

Our equation converted to a square , equated to a number (0.626736111111111).

Since the right part 0.626736111111111 is greater than zero, there are two solutions:


, or






Answer: x=1, -0.583333333333333.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=361 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1, -0.583333333333333. Here's your graph:
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