SOLUTION: Can someone explain how this problem works (if possible step by step so that i can understand it) solve using completing the square, 3x^2-6x=27 the answer is x=1+sqrt(10), 1-sqrt(

Question 198574: Can someone explain how this problem works (if possible step by step so that i can understand it)
solve using completing the square, 3x^2-6x=27 the answer is x=1+sqrt(10), 1-sqrt(10), why?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Subtract 27 from both sides.

Now let's complete the square for the left side expression

Start with the given expression.

Factor out the coefficient . This step is very important: the coefficient must be equal to 1.

Take half of the coefficient to get . In other words, .

Now square to get . In other words,

Now add and subtract inside the parenthesis. Make sure to place this after the "x" term. Notice how . So the expression is not changed.

Group the first three terms.

Factor to get .

Combine like terms.

Distribute.

Multiply.

So after completing the square, transforms to . So .

So is equivalent to .

-------------------------------------------------------------------------

Now let's solve

Start with the given equation.

Add to both sides.

Combine like terms.

Divide both sides by .

Reduce.

Take the square root of both sides.

or Break up the "plus/minus" to form two equations.

or Simplify the square root.

or Add to both sides.

--------------------------------------

Answer:

So the solutions are or .

Note: you can use the quadratic formula to verify your answer.
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