SOLUTION: Complete the square,simplify. Express any complex numbers using i notation {{{2x^2+5x-9=0}}} (2x )(x ) I am stuck because I can not figure out which 2 numbers multiply t

Question 264629: Complete the square,simplify. Express any complex numbers using i notation

(2x )(x )
I am stuck because I can not figure out which 2 numbers multiply to 9 and add to 5.If I use (2x+3)(x+1) I can get 5x but no 9. Please help! This is where I always get stuck while factoring.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
It turns out that you can't factor over the rationals. So let's follow the instructions and complete the square.

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 Subtract from both sides.

or Combine the fractions.

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

Answer:

So the solutions are or .

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