SOLUTION: I need to solve the equation by completing the square. The following is my work but I get the wrong answer. Please let me know where I went wrong. x^2 - 6x +3 = 0 x^2 -6x = -3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: I need to solve the equation by completing the square. The following is my work but I get the wrong answer. Please let me know where I went wrong. x^2 - 6x +3 = 0 x^2 -6x = -3      Log On


   

Question 355000: I need to solve the equation by completing the square. The following is my work but I get the wrong answer. Please let me know where I went wrong.
x^2 - 6x +3 = 0
x^2 -6x = -3
x^2 -6x -3^2 = -3-3^2
x^2 - 6x = -12
(x-6)^2 = sqrt -12
x-6 = sqrt -12
x=6+sqrt -12 and x = 6 - sqrt-12
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's complete the square for the expression x%5E2-6x%2B3


x%5E2-6x%2B3 Start with the given expression.


Take half of the x coefficient -6 to get -3. In other words, %281%2F2%29%28-6%29=-3.


Now square -3 to get 9. In other words, %28-3%29%5E2=%28-3%29%28-3%29=9


x%5E2-6x%2Bhighlight%289-9%29%2B3 Now add and subtract 9. Make sure to place this after the "x" term. Notice how 9-9=0. So the expression is not changed.


%28x%5E2-6x%2B9%29-9%2B3 Group the first three terms.


%28x-3%29%5E2-9%2B3 Factor x%5E2-6x%2B9 to get %28x-3%29%5E2.


%28x-3%29%5E2-6 Combine like terms.


So after completing the square, x%5E2-6x%2B3 transforms to %28x-3%29%5E2-6. So x%5E2-6x%2B3=%28x-3%29%5E2-6.


So x%5E2-6x%2B3=0 is equivalent to %28x-3%29%5E2-6=0.


Now let's solve %28x-3%29%5E2-6=0



%28x-3%29%5E2-6=0 Start with the given equation.


%28x-3%29%5E2=0%2B6Add 6 to both sides.


%28x-3%29%5E2=6 Combine like terms.


x-3=%22%22%2B-sqrt%286%29 Take the square root of both sides.


x-3=sqrt%286%29 or x-3=-sqrt%286%29 Break up the "plus/minus" to form two equations.


x=3%2Bsqrt%286%29 or x=3-sqrt%286%29 Add 3 to both sides.


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Answer:


So the solutions are x=3%2Bsqrt%286%29 or x=3-sqrt%286%29.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim