SOLUTION: How do I solve the equation x plus 4.2 times x equals 26?

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Question 972943: How do I solve the equation x plus 4.2 times x equals 26?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
The question is ambiguous:
Possibility 1:
%28x%2B4.2%29x=26
x%5E2%2B4.2x=26
x%5E2%2B4.2x-26=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4.2x%2B-26+=+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=%284.2%29%5E2-4%2A1%2A-26=121.64.

Discriminant d=121.64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4.2%2B-sqrt%28+121.64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284.2%29%2Bsqrt%28+121.64+%29%29%2F2%5C1+=+3.41452627158489
x%5B2%5D+=+%28-%284.2%29-sqrt%28+121.64+%29%29%2F2%5C1+=+-7.61452627158489

Quadratic expression 1x%5E2%2B4.2x%2B-26 can be factored:
1x%5E2%2B4.2x%2B-26+=+1%28x-3.41452627158489%29%2A%28x--7.61452627158489%29
Again, the answer is: 3.41452627158489, -7.61452627158489. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4.2%2Ax%2B-26+%29

In this case, x=3.41 or x=-7.61
.
Possibility 2:
x%2B4.2x=26
5.2x=26
x=5
In this case, x=5