SOLUTION: The sum of the squares of three consecutive positive even integers is 308. Find the integers using a quadratic equation.

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Question 277506: The sum of the squares of three consecutive positive even integers is 308. Find the integers using a quadratic equation.
Answer by Stitch(470) (Show Source):
You can put this solution on YOUR website!
The equation:
Lets rewrite the equation
Do the multiplication
Simplify
Combine like terms
Subtract 308 from both sides
Notice taht each term is divisible by 3. So factor out a 3
Divide both sides by 3

Now use the quadratic formula

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=400 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8, -12. Here's your graph:

Since the question stated that they were positive integers, 8 is the only answer for X.
So the numbers are: 8, 10, 12