SOLUTION: if a=23, b=x², c=x, d=14, and 2b-3c+d=a, what is the value of x?

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Question 163521: if a=23, b=x², c=x, d=14, and 2b-3c+d=a, what is the value of x?
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
2b-3c+d=a replace the variables b,c,d and a with the equivalent values
2x^2-3x+14=23
Subtract 14 from both sides
2x^2-3x=9
Subtract 9 from both sides
2x^2-3x-9=0 This is a quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-9+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-9=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+81+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+3
x%5B2%5D+=+%28-%28-3%29-sqrt%28+81+%29%29%2F2%5C2+=+-1.5

Quadratic expression 2x%5E2%2B-3x%2B-9 can be factored:
2x%5E2%2B-3x%2B-9+=+2%28x-3%29%2A%28x--1.5%29
Again, the answer is: 3, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-9+%29