SOLUTION: 7.) Solve by completing the square. 2x^2+x-6=0 the answer shows -2,3/2 I am not sure how they got the answer?

Question 165265: 7.) Solve by completing the square.
2x^2+x-6=0
the answer shows -2,3/2 I am not sure how they got the answer?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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 .

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 Take the square root of to get .

or Subtract from both sides.

or Combine like terms.

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

Answer:

So the solutions are or .

Note: the order of the solutions does NOT matter.

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