SOLUTION: how do you solve by completing the square if your problem is: xsq-14x+1=0 ?

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Question 115166: how do you solve by completing the square if your problem is: xsq-14x+1=0 ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-14x%2B1=0 Start with the given equation


x%5E2-14x=-1 Subtract 1 from both sides


Take half of the x coefficient -14 to get -7 (ie -14%2F2=-7)
Now square -7 to get 49 (ie %28-7%29%5E2=49)



x%5E2-14x%2B49=-1%2B49 Add this result (49) to both sides. Now the expression x%5E2-14x%2B49 is a perfect square trinomial.




%28x-7%29%5E2=-1%2B49 Factor x%5E2-14x%2B49 into %28x-7%29%5E2 (note: if you need help with factoring, check out this solver)



%28x-7%29%5E2=48 Combine like terms on the right side

x-7=0%2B-sqrt%2848%29 Take the square root of both sides

x=7%2B-sqrt%2848%29 Add 7 to both sides to isolate x.

So the expression breaks down to
x=7%2Bsqrt%2848%29 or x=7-sqrt%2848%29


So our answer is approximately
x=13.9282032302755 or x=0.0717967697244912

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+15%2C+-10%2C+10%2C+x%5E2-14x%2B1%29+ graph of y=x%5E2-14x%2B1


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=13.9282032302755 and x=0.0717967697244912, so this verifies our answer.