SOLUTION: One number is 10 more than a second number. If the product of the two numbers is 144, what are the two numbers?

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Question 1187272: One number is 10 more than a second number. If the product of the two numbers is 144, what are the two numbers?
Found 3 solutions by ikleyn, Alan3354, MathTherapy:
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
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There are two pairs of such numbers.

One pair is   (8,18).     Another pair is   (-8,-18).
Write and solve the equation
x*(x+10) = 144

Reduce it to the standard quadratic form and then solve by factoring or using the quadratic formula.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
One number is 10 more than a second number. If the product of the two numbers is 144, what are the two numbers?
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Try pairs of integer factors of 144: 2*72, 3*48, etc.
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To solve it algebraically,
x*(x+10) = 144
x^2 + 10x - 144 = 0
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Now, to factor it, you need to find 2 numbers that differ by 10 and have a product of 144.
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If they were not integers, you would have to use the quadratic equation or complete the square.
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eg:
One number is 10 more than a second number. If the product of the two numbers is 154, what are the two numbers?
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x^2 + 10x - 154 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B10x%2B-154+=+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=%2810%29%5E2-4%2A1%2A-154=716.

Discriminant d=716 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+716+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+716+%29%29%2F2%5C1+=+8.37908816025965
x%5B2%5D+=+%28-%2810%29-sqrt%28+716+%29%29%2F2%5C1+=+-18.3790881602597

Quadratic expression 1x%5E2%2B10x%2B-154 can be factored:
1x%5E2%2B10x%2B-154+=+%28x-8.37908816025965%29%2A%28x--18.3790881602597%29
Again, the answer is: 8.37908816025965, -18.3790881602597. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B-154+%29

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The solver always says it can be factored, but not necessarily with integers.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

One number is 10 more than a second number. If the product of the two numbers is 144, what are the two numbers?
Correct answer: