SOLUTION: how do I find the value/values of z in the equation z^2-4z+4=0

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Question 174884: how do I find the value/values of z in the equation z^2-4z+4=0
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

z%5E2-4z%2B4=0 Start with the given equation.


Notice we have a quadratic equation in the form of az%5E2%2Bbz%2Bc where a=1, b=-4, and c=4


Let's use the quadratic formula to solve for z


z+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


z+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-4, and c=4


z+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


z+=+%284+%2B-+sqrt%28+16-4%281%29%284%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


z+=+%284+%2B-+sqrt%28+16-16+%29%29%2F%282%281%29%29 Multiply 4%281%29%284%29 to get 16


z+=+%284+%2B-+sqrt%28+0+%29%29%2F%282%281%29%29 Subtract 16 from 16 to get 0


z+=+%284+%2B-+sqrt%28+0+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


z+=+%284+%2B-+0%29%2F%282%29 Take the square root of 0 to get 0.


z+=+%284+%2B+0%29%2F%282%29 or z+=+%284+-+0%29%2F%282%29 Break up the expression.


z+=+%284%29%2F%282%29 or z+=++%284%29%2F%282%29 Combine like terms.


z+=+2 or z+=+2 Simplify.


So the solution is z=2 (with a multiplicity of 2)


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how do I find the value/values of z in the equation z^2-4z+4=0
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z^2 - 4z + 4 = 0
Factor to get:
(z-2)(z-2) = 0
Since the product is zero, one of the factors must be zero:
z-2 = 0
Therefore z = 2
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Cheers,
Stan H.