Solve by completing the square:  x²-10x = 11   Please help! I've done every other question on my assignment but I've been over and over this ones and can't figure it out!

Expert Answers

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x^2 -10x =11

Now we will add and subtract [(X's coefficient)/2]^2

We know that X's coefficient is 10

==> Then, we will add (10/2)^2 = 5^2 = 25 to both sides.

==> x^2 -10x +25 = 11 + 25

==> x^2 -10x +25 = 36

Now we will rewrite the expression as a complete square.

==> (x-5)^2 = 36

Now to solve, we will take the square root of both sides.

==> l x -5 l = l6l

==> x-5 = 6 ==> x = 11

==> -(x-5) = 6 ==> -x+5 = 6 ==>  -x = 1 ==> x = -1

Then we have two solutions:

x = { -1, 11}

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