SOLUTION: solve for x by completing the square: x^2+6x=2

Question 75813: solve for x by completing the square: x^2+6x=2
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!

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The process goes as follows:
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First look at the coefficient or multiplier of the x term. Take half of that coefficient,
square the result, and add that number to both sides of the equation.
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For this problem, the coefficient of the x term is +6. Take half of that and you have +3.
Square the +3 and you get +9. Add +9 to both sides of the equation to get:
.

.
You have now made the left side of the equation a perfect square. The term that is squared
is where the +3 comes from half the coefficient of the x term. So the equation
can be written as:
.

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Note that the 11 comes from adding the 2 and 9 on the right side.
.
Now take the square root of both sides and you get:
.
and
.
Finally, subtract 3 from both sides to get rid of the +3 that is on the left side. When
you do you get:
.
and
.
and those are the two values of x that satisfy the equation of the original problem.
.
Hope this helps you to see and understand the process that you use to solve quadratic
equations by completing the square. The process remains the same, only the numbers
change for different quadratic equations.
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