SOLUTION: Solve the following quadratic equation by completing the square. I get the first part then i get lost, please help me. x^2-6x-3=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the following quadratic equation by completing the square. I get the first part then i get lost, please help me. x^2-6x-3=0      Log On


   

Question 124289: Solve the following quadratic equation by completing the square. I get the first part then i get lost, please help me. x^2-6x-3=0
Found 2 solutions by edjones, jim_thompson5910:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-6x-3=0
x^2-6x =3
x^2-6x+9=3+9 completing the square.
(x-3)^2=12
x-3=+-sqrt(12)
x=3+-sqrt(4*3)
x=3+2sqrt(3)
x=3-2sqrt(3)
.
Ed

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


y%2B3=x%5E2-6+x Add 3 to both sides


Take half of the x coefficient -6 to get -3 (ie %281%2F2%29%28-6%29=-3).

Now square -3 to get 9 (ie %28-3%29%5E2=%28-3%29%28-3%29=9)




y%2B3=x%5E2-6x%2B9-9 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 9 does not change the equation



y%2B3=%28x-3%29%5E2-9 Now factor x%5E2-6x%2B9 to get %28x-3%29%5E2



y=%28x-3%29%5E2-9-3 Now add %2B3 to both sides to isolate y


y=%28x-3%29%5E2-12 Combine like terms



%28x-3%29%5E2-12=0 Now to solve for x, let y=0


%28x-3%29%5E2=%2B12 Add 12 to both sides



Take the square root of both sides


Simplify sqrt%2812%29 to get 2sqrt%283%29


Add 3 to both sides



So our answers are

or