2x2+12x+1 = 0
By dividing all terms in the quadratic equation by 2 will make completing the square easier to work out:
x2+6x+0.5 = 0
(x+3)2+0.5 = 0
(x+3)2-9+0.5 = 0
(x+3)2-8.5 = 0
(x+3)2 = 8.5
x+3 = the square root of 8.5
x = -3 and plus or minus the square root of 8.5
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use algebra and then factor... x= -9 and 9
This quadratic equation has no solutions because the discriminant is less than zero.
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It cannot be solved because the discriminant of the quadratic equation is less than zero
If you aren't dealing with algebra, such as x2+3x+21, then completing the square wont be able to solve the porblem, however if you are using algebra, and you cannot factorise, then completing the square will always work