Question 28000: Using the quadratic equation x2-3x+2=0 perform the following tasks:
solve by factoring.
solve by completing the square. Since it is x square, should i devide both sides by x?
solve by using the quadratic equasion.
I don't necesarily want it answered, I just need to know how to do these equations.
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! Using the quadratic equation x2-3x+2=0 perform the following tasks:
solve by factoring.
solve by completing the square. Since it is x square, should i devide both sides by x?
solve by using the quadratic equasion.
I don't necesarily want it answered, I just need to know how to do these equations.
completing the square method
x2-3x+2=0
[x^2-2X(3/2)X(x)]+2=0
Notice that the first two terms have been brought under the structure a^2 -2ab. So you need b^2 to complete the square and here b^2-(3/2)^2 = 9/4
Therefore
[x^2-2X(3/2)X(x)+(9/4-9/4)]+2=0
[x^2-2X(3/2)X(x)+(9/4]+(-9/4+2)=0
(x-3/2)^2 = 9/4-2 = 1/4
Taking the sqroot
(x-3/2)= +1/2 or -1/2
(x-3/2)= +1/2 gives x = 1/2+3/2 = 2
(x-3/2)= -1/2 gives x = -1/2+3/2 = 1
Answer: x = 2 and x=1
solve by using the quadratic equasion
x2-3x+2=0
x2+[(-2x)+(-x)]+2=0
[splitting the middle term into two parts
whose multiplication is the product of the square term and the constant term.
-3x = (-2x) + (-x) so that (-2x)X(-x) = +(2x^2) = (x^2)X(2)]
x2-2x-x+2=0 (you may straight away write this without writing the previous. the previous step is for your self study)
(x2-2x)-x+2=0
x(x-2)-(x-2)=0 (why pull out -1 ? just to get (x-2) as a common factor.)
xp-p=0 where p = (x-2)
p(x-1) = 0
(x-2)(x-1) = 0
(x-2) = 0 gives x = 2 and (x-1) = 0 gives x = 1
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