SOLUTION: K is between J and L JK=2x^2+3 KL=7x+4 JL=2x+10 Find JK I have solved to 2x^2+5X=3, but that makes no sense and am lost. Thanks for any help.

Question 490208: K is between J and L JK=2x^2+3 KL=7x+4 JL=2x+10 Find JK
I have solved to 2x^2+5X=3, but that makes no sense and am lost. Thanks for any help.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
K is between J and L
this means that JK + KL = JL

JK is equal to 2x^2 + 3
KL is equal to 7x+4
JL is equal to 2x+10

since JK + KL = JL, this means that:
2x^2 + 3 + 7x+4 = 2x+10

you want to solve for x.
once you solve for x, then you can solve for the value of JK.

your equation to work with is:
2x^2 + 3 + 7x + 4 = 2x + 10
subtract 2x from both sides of the equation and subtract 10 from both sides of the equation to get:
2x^2 + 3 + 7x + 4 - 2x - 10 = 0
combine like terms to get:
2x^2 + 5x - 3 = 0
this is a quadratic equation that can be solved for the value of x.
the factors to this equation are:
(2x - 1) * (x + 3) = 0
this equation is true if (2x - 1) = 0 or (x + 3) = 0 or both are equal to 0.
solving for 2x - 1 = 0 gets x = 1/2
solving for x + 3 = 0 gets x = -3

since we are talking about the length of JK, KL, AND JL, then the length must be positive so the only answer that is acceptable is x = 1/2

when x = 1/2, we get:

JK = 2x^2 + 3 which results in JK = 3.5
KL = 7x + 4 which results in KL = 7.5
JL = 2x + 10 which results in JL = 11

since JK + KL = JL, then we should get 11 = 11
JK + KL = 3.5 + 7.5 = 11
we're good.

the value of x is confirmed as good which results in JK = 3.5 which answers the question.

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