SOLUTION: Solve by completing the square. x^2 = 5x + 2

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Question 104367: Solve by completing the square.
x^2 = 5x + 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+=+5x+%2B+2 Start with the given equation


x%5E2-5x=2 Subtract 5x from both sides


Take half of the x coefficient -5 to get -2.5 (ie -5%2F2=-2.5)
Now square -2.5 to get 6.25 (ie %28-2.5%29%5E2=6.25)



x%5E2-5x%2B6.25=2%2B6.25 Add this result (6.25) to both sides. Now the expression x%5E2-5x%2B6.25 is a perfect square trinomial.




%28x-2.5%29%5E2=2%2B6.25 Factor x%5E2-5x%2B6.25 into %28x-2.5%29%5E2



%28x-2.5%29%5E2=8.25 Combine like terms on the right side

x-2.5=0%2B-sqrt%288.25%29 Take the square root of both sides

x=2.5%2B-sqrt%288.25%29 Add 2.5 to both sides to isolate x.

So the expression breaks down to
x=2.5%2Bsqrt%288.25%29 or x=2.5-sqrt%288.25%29


So our answer is approximately
x=5.37228132326901 or x=-0.372281323269014

Here is visual proof

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


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=5.37228132326901 and x=-0.372281323269014, so this verifies our answer.