SOLUTION: One number is 2 more than 5 times another. Their product is 3. Find the numbers.

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Question 225116: One number is 2 more than 5 times another. Their product is 3. Find the numbers.
Answer by drj(1380) About Me  (Show Source):
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One number is 2 more than 5 times another. Their product is 3. Find the numbers.

Step 1. Let x be one number

Step 2. Let 2+5x be the other number since its 2 more than 5 times the first number.

Step 3. Then, x%282%2B5x%29=3 since their product is 3.

Step 4. Turn this equation into a quadratic one in standard form as follows:

x%282%2B5x%29=3

2x%2B5x%5E2=3

Subtract 3 from both sides

2x%2B5x%5E2-3=3-3

Simplify and arrange in descending order to get our quadratic equation

5x%5E2%2B2x-3=0

Step 4. To solve, use the quadratic formula given as

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

where a=5, b=2, and c=-3

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B2x%2B-3+=+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=%282%29%5E2-4%2A5%2A-3=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+64+%29%29%2F2%5C5+=+0.6
x%5B2%5D+=+%28-%282%29-sqrt%28+64+%29%29%2F2%5C5+=+-1

Quadratic expression 5x%5E2%2B2x%2B-3 can be factored:
5x%5E2%2B2x%2B-3+=+5%28x-0.6%29%2A%28x--1%29
Again, the answer is: 0.6, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B2%2Ax%2B-3+%29



With x=0.6 then 2+5x=2+5*0.6=5

With x=-1 then 2+5*(-1)=-3.

Step 5. ANSWER: The numbers are 0.6 and 5 as one pair and -1 and -3 as the other pair of numbers.

I hope the above steps and explanation 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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV