SOLUTION: (x+3)^2+27x+60=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: (x+3)^2+27x+60=0      Log On


   

Question 311290: (x+3)^2+27x+60=0
Found 2 solutions by Fombitz, fractalier:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B3%29%5E2%2B27x%2B60=0
%28x%2B3%29%5E2%2B27%28x%2B3%29%2B60-81=0
%28x%2B3%29%5E2%2B27%28x%2B3%29-21=0
Let u=x%2B3
u%5E2%2B27u-21=0
Use the quadratic formula,
u+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
u+=+%28-27+%2B-+sqrt%28+27%5E2-4%2A1%2A%28-21%29+%29%29%2F%282%2A1%29+
u+=+%28-27+%2B-+sqrt%28+729%2B84+%29%29%2F%282%29+
u+=+%28-27+%2B-+sqrt%28+813+%29%29%2F%282%29+
x%2B3+=+%28-27+%2B-+sqrt%28+813+%29%29%2F%282%29+
x+=+%28-33+%2B-+sqrt%28+813+%29%29%2F%282%29+or approximately,
x=-30.8 and x=-2.2
.
.
.
+graph%28+300%2C+300%2C+-45%2C+5%2C+-50%2C+50%2C+%28x%2B3%29%5E2%2B27x%2B60%29+

Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Okay, from (x+3)^2+27x+60=0,
let's expand, collect like terms, and solve...here goes...
x^2 + 6x + 9 + 27x + 60 = 0
x^2 + 33x + 69 = 0
We would like to factor this by finding factors of 69 that add to 33, but there aren't any, so we'll have to use the quadratic formula...
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
so that
x = [-33 +- sqrt(33^2 - 4*1*69)] / 2
x = [-33 +- sqrt(1089 - 276)] / 2
x = [-33 +- sqrt(813)] / 2