SOLUTION: Please help me solve this word problem { { { Let "x" be the first of three consecutive even integers. If the sum of the squares of the first and second is eighty-four more than the

Question 587484: Please help me solve this word problem { { { Let "x" be the first of three consecutive even integers. If the sum of the squares of the first and second is eighty-four more than the square of the largest, find all three integers.
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!
x, x+2, x+4
x^2 + (x+2)^2 = (x+4)^2 + 84
x^2 + x^2 + 4x + 4 = x^2 + 8x + 16 + 84
2x^2 + 4x + 4 = x^2 + 8x + 100
x^2 - 4x - 96 = 0

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: 12, -8. Here's your graph:

x = 12, -8
technically both {-8, -6, -4} AND {12, 14, 16} satisfy
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