SOLUTION: One half the square of a number increased by three timesthe number is equal to 8. Find the number

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Question 688748: One half the square of a number increased by three timesthe number is equal to 8. Find the number
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
X%5E2%2F2+%2B+3X+=+8
Subtract 8 from both sides
X%5E2%2F2+%2B+3X+-8+=+0
Multiply everthing by 2
X%5E2+%2B+6X+-+16+=+0
Use the quadratic equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aX%5E2%2BbX%2Bc=0 (in our case 1X%5E2%2B6X%2B-16+=+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=%286%29%5E2-4%2A1%2A-16=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+100+%29%29%2F2%5Ca.

X%5B1%5D+=+%28-%286%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+2
X%5B2%5D+=+%28-%286%29-sqrt%28+100+%29%29%2F2%5C1+=+-8

Quadratic expression 1X%5E2%2B6X%2B-16 can be factored:
1X%5E2%2B6X%2B-16+=+1%28X-2%29%2A%28X--8%29
Again, the answer is: 2, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-16+%29


The two answers are: 2 & -8