SOLUTION: 2x^2-4x-7=0 solve by completing the square

Question 147093: 2x^2-4x-7=0 solve by completing the square
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression

Factor out the leading coefficient

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Notice how . Since we're adding 0, we're not changing the equation.

Now factor to get

Combine like terms

Distribute

Multiply

So after completing the square, becomes .

In other words,

So is equivalent to

Start with the given equation

Add 9 to both sides

Divide both sides by 2

Take the square root of both sides

Add 1 to both sides

or Break up the plus/minus

or Simplify

or Rationalize the denominator

So our answers are or
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Step 1: Add the constant term to both sides

Step 2: Divide both sides by the lead coefficient

Step 3: Divide the coefficient on the 1st degree term by 2 (), square the result , then add it to both sides

Step 4: Factor the perfect square on the left

Step 5: Take the square root of both sides

or

Step 6: Add the constant term on the left to both sides

Step 7: Simplify

(Left as an exercise for the student. Remember to rationalize your denominator)
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