SOLUTION: I need to solve by completing the square x^2-4X+45 I believe I would first divide by not sure by what since 45 is neg not positive. Thank you for the help walking me through th

Algebra ->  Equations -> SOLUTION: I need to solve by completing the square x^2-4X+45 I believe I would first divide by not sure by what since 45 is neg not positive. Thank you for the help walking me through th      Log On


   

Question 762460: I need to solve by completing the square
x^2-4X+45 I believe I would first divide by not sure by what since 45 is neg not positive. Thank you for the help walking me through this one so I can do the rest.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You could Complete the Square but you have nothing to solve. You show no equation nor inequality.

Why you say 45 is neg not positive. 45 is positive.

The missing square term for x^2-4x+45 is %28%28-4%29%2F2%29%5E2=4. You will both ADD and SUBTRACT 4 to the expression.

%28x%5E2-4x%2B4%29%2B45-4
highlight%28%28x-2%29%5E2+%2B+41%29
That is as far as you can go.

In case you in fact have x%5E2-4X%2B45=0, then you CAN solve for x easily. You equivalently have %28x-2%29%5E2+%2B+41=0, and the usefulness of Completing the Square becomes obvious (that the treated equation is now easy to solve).

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2+-+4x+%2B+45+=+0+
Subtract +45+ from both sides
+x%5E2+-+4x+=+-45+
Take 1/2 of the coefficient of the x
term, square it, and add it to both sides
+x%5E2+-+4x+%2B+%28+-4%2F2+%29%5E2+=+-45+%2B+%28+-4%2F2+%29%5E2+
Note that when minus is squared, it becomes positive
+x%5E2+-+4x+%2B+%28+-4%2F2+%29%5E2+=+-45+%2B+%28+-4%2F2+%29%5E2+
+x%5E2++-+4x+%2B+4+=+-45+%2B+4+
+x%5E2+-+4x+%2B+4+=+-41+
+%28+x+-+2+%29%5E2+=+-41+
Take the square root of both sides
+x+-+2+=+sqrt%28+41+%29%2Ai++
+x+=+2+%2B+sqrt%28+41+%29%2Ai+
and, also
+x+-+2+=+-sqrt%28+41+%29%2Ai++
+x+=+2+-+sqrt%28+41+%29%2Ai+
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This would have been much easier if the equation was
+x%5E2+-+4x+-+45+ -are you sure of the +%2B45+?