SOLUTION: Solve each of the following quadratic equations by completing the square. x2 - 6x - 3 = 0

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Question 115422: Solve each of the following quadratic equations by completing the square.
x2 - 6x - 3 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-6x-3=0 Start with the given equation


x%5E2-6x=3 Add 3 to both sides


Take half of the x coefficient -6 to get -3 (ie -6%2F2=-3)
Now square -3 to get 9 (ie %28-3%29%5E2=9)



x%5E2-6x%2B9=3%2B9 Add this result (9) to both sides. Now the expression x%5E2-6x%2B9 is a perfect square trinomial.




%28x-3%29%5E2=3%2B9 Factor x%5E2-6x%2B9 into %28x-3%29%5E2 (note: if you need help with factoring, check out this solver)



%28x-3%29%5E2=12 Combine like terms on the right side

x-3=0%2B-sqrt%2812%29 Take the square root of both sides

x=3%2B-sqrt%2812%29 Add 3 to both sides to isolate x.

So the expression breaks down to
x=3%2Bsqrt%2812%29 or x=3-sqrt%2812%29


So our answer is approximately
x=6.46410161513775 or x=-0.464101615137754

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-6x-3%29+ graph of y=x%5E2-6x-3


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=6.46410161513775 and x=-0.464101615137754, so this verifies our answer.