SOLUTION: Solve by completing the square 3x^2+5x-1=0

Question 171916: Solve by completing the square
3x^2+5x-1=0
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the left 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 .

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

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 Subtract from both sides.

or Combine the fractions.

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

Answer:

So the solutions are or .

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
First add to both sides

Now divide both sides by

Take 1/2 of the coefficient of , square it
and add it to both sides

The thing to realize at this point is that the
left side is a perfect square. It is
, so

Take the square root of both sides

Solve for

and

Both answers are correct
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