SOLUTION: Can someone please assist me with detailed step by step instructions on how to complete this problem? Your assistance and time is greatly appreciated. Solve by completing the sq

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can someone please assist me with detailed step by step instructions on how to complete this problem? Your assistance and time is greatly appreciated. Solve by completing the sq      Log On


   

Question 90251: Can someone please assist me with detailed step by step instructions on how to complete this problem? Your assistance and time is greatly appreciated.
Solve by completing the square.
x2 = 5x + 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+=+5x+%2B+2

x2+-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.