SOLUTION: child a is 4 years older than b. the product of their ages is 140. the equation is x(x-4)=140 how do you solve for x?

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Question 218658: child a is 4 years older than b. the product of their ages is 140.
the equation is x(x-4)=140
how do you solve for x?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Child a is 4 years older than b. The product of their ages is 140.

The equation is x(x-4)=140

how do you solve for x?

Step 1. Form a quadratic equation to get x%5E2-4x=140. Then subtract 140 from both sides of the equation

x%5E2-4x-140=140-140

x%5E2-4x-140=0

x%5E2-4x-140=%28x%2B10%29%28x-14%29=0

Or x=-10 and x=14. We need to select x=14 for positive ages.

ANSWER: x is 14 hears old


Step 2. We can also se the quadratic formula given as

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=-4 and c=-140

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%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=%28-4%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-%28-4%29%2Bsqrt%28+576+%29%29%2F2%5C1+=+14
x%5B2%5D+=+%28-%28-4%29-sqrt%28+576+%29%29%2F2%5C1+=+-10

Quadratic expression 1x%5E2%2B-4x%2B-140 can be factored:
1x%5E2%2B-4x%2B-140+=+1%28x-14%29%2A%28x--10%29
Again, the answer is: 14, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-140+%29



Same result as before...

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J