SOLUTION: Solve the quadratic equation by completing the square: 3x^2+6x-4=0

Question 169929: Solve the quadratic equation by completing the square:
3x^2+6x-4=0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the right side of the equation.

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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Start with the given equation.

Add to both sides.

Combine like terms.

Divide both sides by .

Take the square root of both sides.

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

or Simplify the square root.

or Subtract from both sides.

or Combine the fractions.

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Answer:

So the solutions are or .

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