SOLUTION: Could someone please help me with this equation? Solve this quadratic equation by completing the square. {{{2x^2+10x+11=0}}}

Question 100449: Could someone please help me with this equation? Solve this quadratic equation by completing the square.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

Subtract 11 from both sides
Factor out the leading coefficient 2. This step is important since we want the coefficient to be equal to 1.

Take half of the x coefficient 5 to get 2.5 (ie )
Now square 2.5 to get 6.25 (ie )

Add this result (6.25) to the expression inside the parenthesis. Now the expression is a perfect square trinomial. Now add the result (6.25)(2) (remember we factored out a 2) to the right side.

Factor into

Multiply 6.25 and 2 to get 12.5

Combine like terms on the right side

Divide both sides by 2

Take the square root of both sides

Subtract 2.5 from both sides to isolate x.

So the expression breaks down to
or

So our answer is approximately
or

Here is visual proof

graph of

When we use the root finder feature on a calculator, we would find that the x-intercepts are and , so this verifies our answer.

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