SOLUTION: The solution for the equation, {{{ x+4 = sqrt (x^3-2x^2-5)+3 }}}, to the nearest hundredth, is?

Algebra ->  Functions -> SOLUTION: The solution for the equation, {{{ x+4 = sqrt (x^3-2x^2-5)+3 }}}, to the nearest hundredth, is?      Log On


   

Question 950375: The solution for the equation, +x%2B4+=+sqrt+%28x%5E3-2x%5E2-5%29%2B3+, to the nearest hundredth, is?
Found 2 solutions by Fombitz, josgarithmetic:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x-1=sqrt%28x%5E3-2x%5E2-5%29
%28x%2B1%29%5E2=x%5E3-2x%5E2-5
x%5E2%2B2x%2B1=x%5E3-2x%5E2-5
x%5E3-3x%5E2-2x-6=0
.
.
graph%28300%2C300%2C-5%2C5%2C-5%2C5%2Cx%5E3-3x%5E2-2x-6%29
.
.
Using Newton's method with a starting value of x=4,
.
x=3.91


Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You may need some rational coefficient polynomial skills for this one.

sqrt%28x%5E3-2x%5E2-5%29=x%2B1

x%5E3-2x%5E2-5=x%5E2%2B2x%2B1

x%5E3-3x%5E2-2x-6=0

Can you find the roots of this equation? Maybe rational roots theorem, maybe not.

Checking in Google's graphing feature, root is 3.905, very near to.