SOLUTION: This problem is so difficult! I honestly don't know what to do. Can someone please, please answer this question: Solve by completing the square: x^2=5x+2 Thank you.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: This problem is so difficult! I honestly don't know what to do. Can someone please, please answer this question: Solve by completing the square: x^2=5x+2 Thank you.      Log On


   

Question 90551: This problem is so difficult! I honestly don't know what to do. Can someone please, please answer this question:
Solve by completing the square: x^2=5x+2
Thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2=5x%2B2
x%5E2-5x=2 Subtract 5x from both sides

1%28x%5E2-5x%29=2 Factor out 1



Take half of -5 to get -2.5 (ie -5%2F2=-2.5)
Now square -2.5 to get 6.25 (ie -2.5%5E2=6.25)



1%28x%5E2-5x%2B6.25%29=2 Add this result (6.25) inside the parenthesis

1%28x%5E2-5x%2B6.25%29=2%2B6.25%281%29 Add 6.25(1) to the other side (remember we factored out a 1)

Now the left side is a complete square

1%28x-2.5%29%5E2=2%2B6.25%281%29 Factor the left side

1%28x-2.5%29%5E2=8.25 Multiply and 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

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.