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Place the following steps in order to complete the square and solve the quadratic equation x2-6x+7=0

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1 vote

Answer:

The solved expression is
x=3+√(2) and
x=3-√(2)

Therefore
x=3\pm√(2)

Explanation:

Given quadratic equation is
x^2-6x+7=0

To solve the given equation by using completing the square :


x^2-6x+7=0

Rewritting the above equation as below :


x^2-6x+7+2-2=0


(x^2-6x+7+2)-2=0


(x^2-6x+9)-2=0


(x^2-6x+3^2)-2=0


(x^2-2(x)(3)+3^2)-2=0 ( it is of the form of
(a-b)^2=a^2-2ab+b^2 heere a=x and b=3 )


(x-3)^2-2=0


(x-3)^2=2

Taking square root on both sides we get


√((x-3)^2)=\pm√(2)


x-3=\pm√(2)


x=\pm√(2)+3


x=3\pm√(2)

Therefore
x=3+√(2) and
x=3-√(2)

User Ed Barahona
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