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) About Me  (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 = %28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F%282a%29

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 = %289+%2B-+sqrt%28249%29%29%2F%286%29 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 k+=+sqrt%28x%29

square both sides of this equation to get x+=+k%5E2

your answers of:

k = 4.12995564
k = -1.12995564

become:

x = 17.05653359
x = 1.276799748

plug these into the original equation of 3x+-9%2Asqrt%28x%29+-+14+=+0 to confirm they are good.

the value of 17.05653359 is confirmed as good since sqrt%2817.05653359%29 = +/- 4.12995564 except that you have to use the positive square root only.

the value of 1.276799748 is confirmed as good since sqrt%281.276799748%29 = +/- 1.12995564 except that you have to use the negative square root only.