SOLUTION: the square of a positive number increased by 4 times the number is equal to 140 find the number

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Question 955258: the square of a positive number increased by 4 times the number is equal to 140 find the number
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the number
x%5E2%2B4x=140
x%5E2%2B4x-140=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-140+=+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%29%5E2-4%2A1%2A-140=576.

Discriminant d=576 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+576+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+10
x%5B2%5D+=+%28-%284%29-sqrt%28+576+%29%29%2F2%5C1+=+-14

Quadratic expression 1x%5E2%2B4x%2B-140 can be factored:
1x%5E2%2B4x%2B-140+=+1%28x-10%29%2A%28x--14%29
Again, the answer is: 10, -14. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-140+%29

x=10 ANSWER: The number is 10