SOLUTION: hi, solve by completing the square x^2-2x-7=0. can you please help me? thank you!!

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Question 109459This question is from textbook algebra2 with trigonometry
: hi,
solve by completing the square x^2-2x-7=0. can you please help me? thank you!! This question is from textbook algebra2 with trigonometry

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-2x-7=0 Start with the given equation


x%5E2-2x=7 Add 7 to both sides


Take half of the x coefficient -2 to get -1 (ie -2%2F2=-1)
Now square -1 to get 1 (ie %28-1%29%5E2=1)



x%5E2-2x%2B1=7%2B1 Add this result (1) to both sides. Now the expression x%5E2-2x%2B1 is a perfect square trinomial.




%28x-1%29%5E2=7%2B1 Factor x%5E2-2x%2B1 into %28x-1%29%5E2 (note: if you need help with factoring, check out this solver)



%28x-1%29%5E2=8 Combine like terms on the right side

x-1=0%2B-sqrt%288%29 Take the square root of both sides

x=1%2B-sqrt%288%29 Add 1 to both sides to isolate x.

So the expression breaks down to
x=1%2Bsqrt%288%29 or x=1-sqrt%288%29


So our answer is approximately
x=3.82842712474619 or x=-1.82842712474619

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-2x-7%29+ graph of y=x%5E2-2x-7


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=3.82842712474619 and x=-1.82842712474619, so this verifies our answer.