SOLUTION: Solve by completing the square. 2x^2 – 6x – 3 = 0
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Question 103658: Solve by completing the square. 2x^2 – 6x – 3 = 0
Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve by completing the square.
:
2x^2 – 6x – 3 = 0
:
When completing the square, we need the coefficient of x^2 to be; divide eq by 2:
x^2 - 3x - = 0
:
x^2 - 3x + ___ =
:
Find the value that will make it a perfect square, divide the coefficient of x by 2 and square it; add to both sides:
=
we have:
x^2 - 3x + = +
:
x^2 - 3x + = + ; use the common denominator on the right
:
x^2 - 3x + = +
:
(x - )^2 =
:
x - = +/- ; square root of both sides
:
x - = +/- ; extract the square root of 1/4
:
x = +/- ; Add to both sides
Same as:
x = ;
Two solutions:
x =
and
x =
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation
Add 3 to 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 -3 to get -1.5 (ie )
Now square -1.5 to get 2.25 (ie )
Add this result (2.25) to the expression inside the parenthesis. Now the expression is a perfect square trinomial. Now add the result (2.25)(2) (remember we factored out a 2) to the right side.
Factor into
Multiply 2.25 and 2 to get 4.5
Combine like terms on the right side
Divide both sides by 2
Take the square root of both sides
Add 1.5 to 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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