SOLUTION: The problem is X3 + X2 is less than or equal to 4X +4 How do you derive the quadratic formula using "complete the square"? Thank you Sandra Gardner

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: The problem is X3 + X2 is less than or equal to 4X +4 How do you derive the quadratic formula using "complete the square"? Thank you Sandra Gardner      Log On


   

Question 64103: The problem is
X3 + X2 is less than or equal to 4X +4
How do you derive the quadratic formula using "complete the square"?
Thank you
Sandra Gardner
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is
X^3 + X^2 is less than or equal to 4X +4
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x^3+x^2<=4x+4
x^3+x^2-4x-4<=0
x^2(x+1)-4(x+1)<=0
(x+1)(x^2-4)=0
(x+1)(x-2)(x+2)=0
x=-1 or x=2 or x=-2
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How do you derive the quadratic formula using "complete the square"?
ax^2+bx+c=0
ax^2+by+? = -c+?
Complete the square:
a(x^2+(b/a)x+(b/2a)^2)=-c+a(b/2a)^2
a(x+(b/2a))^2 = -c+ab^2/4a
(x+b/2a)^2 =(b^2-4ac)/4a^2
Take the square root to get:
x+(b/2a)=+-sqrt[(b^2-4ac)/4a^2]
x=-(b/2a)+-sqrt[b^2-4ac]/2a
x=[-b+-sqrt(b^2-4ac)]/2a
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Cheers,
Stan H.