SOLUTION: 1.What number needs to be added to both sides of the equation in order to complete the square? x^2-18x=17 2.What are the roots of the equation? 4x^3-20x^2+24x=0 3.What

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 1.What number needs to be added to both sides of the equation in order to complete the square? x^2-18x=17 2.What are the roots of the equation? 4x^3-20x^2+24x=0 3.What       Log On


   

Question 1057728: 1.What number needs to be added to both sides of the equation in order to complete the square?
x^2-18x=17
2.What are the roots of the equation?
4x^3-20x^2+24x=0
3.What are the roots of the equation?
x^6(6x-11)(7x-8)=0
4.Factor This.
6x^2-42x-54
5.Solve as exact values.
x^2-9x+3=0
6.What is the solution of the equation over the complex numbers as exact values?
x^2+20=0
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-18x+81 =17+81. Take half the middle term and square it. This will be (x-9)^2=98, x-9=sqrt(98)=7 sqrt (2), and x=9+/-7 sqrt (2).
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4x^3-20x^2+24x=0
factor out a 4x
4x(x^2-5x+6)=0
4x(x-2)(x-3)=0
roots are 0,2,3
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C4x%5E3-20x%5E2%2B24x%29
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x^6(6x-11)(7x-8)=0
Set the factors equal to 0 and solve for x, which will be 0, 11/6, and 8/7.
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6x^2-42x-54
6(x^2-7x-9)
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x^2-9x+3=0
x=(1/2)(9 +/-sqrt(81-12))=(1/2)(9+sqrt(69)) and (1/2)(9-sqrt (69))
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x^2=-20
x=+/-sqrt(-4)*sqrt(5)
+/- 2i sqrt (5)