SOLUTION: Solve for x/complete the square: 5x^2+2x√10=1?

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Question 630719: Solve for x/complete the square: 5x^2+2x√10=1?
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!

First I am going to use the Commutative and Associative Properties on the middle term so that it is something times x, with the x at the end:


It is easier to complete a square if the coefficient of the squared term is 1. So we will divide both sides by 5 (or multiply by 1/5):


Next we find half of the middle coefficient. Half of is

Next we square the "half" and add that number to both sides. . Adding 2/5 to each side we get:

which simplifies to:

The left side is a completed square after what we have done. It is (x + the "half" we found earlier) squared:

Now we find the square root of each side:

= +
Rationalizing the denominator on the right:
= +
= +
= +
= +
Adding to each side:

which simplifies to:
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