SOLUTION: How do you solve the equation: 0=3x-9√x-14?
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Question 274516: How do you solve the equation: 0=3x-9√x-14?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
equation is:
0=3x-9√x-14?
let k = sqrt(x)
equation becomes:
0 = 3k^2 - 9k - 14
this is a quadratic equation.
factor using the quadratic formula of k =
a = 3
b = -9
c = -14
2a = 6
-b = 9
b^2 = 81
4ac = -168
b^2 - 4ac = 81 + 168 = 249
quadratic formula becomes k = which becomes:
k = (9 +/- 5.77973384)/6 which becomes:
k = 4.12995564
k = -1.12995564
confirm these are correct by plugging into the equation of 3k^2 - 9k - 14 = 0.
once confirmed (done already), then you need to translate the k to x using the formula you used to derive k.
that formula was
square both sides of this equation to get
your answers of:
k = 4.12995564
k = -1.12995564
become:
x = 17.05653359
x = 1.276799748
plug these into the original equation of to confirm they are good.
the value of 17.05653359 is confirmed as good since = +/- 4.12995564 except that you have to use the positive square root only.
the value of 1.276799748 is confirmed as good since = +/- 1.12995564 except that you have to use the negative square root only.
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