SOLUTION: Please help me solve this equation 5-5 Completing the Square Solving a quadratic equation if the coefficient of x^2 is NOT 1 3x^2+12x-9=0

Question 191084: Please help me solve this equation
5-5 Completing the Square
Solving a quadratic equation if the coefficient of x^2 is NOT 1

3x^2+12x-9=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First, let's complete the square for the left side of the equation

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 .

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Now let's solve

Start with the given equation.

Add 21 to both sides

Divide both sides by .

Reduce.

Take the square root of both sides. (note: don't forget the "plus/minus")

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

or Subtract from both sides.

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Answer:

So the solutions are or .
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