SOLUTION: Solve by completing the square: 4x^2 + 2x - 3 = 0
4x^2 + 2x = 3
x^2 + 2/4x = 3/4
Square one-half of the of the x-coefficient and then add it to both sides
1/2 of 2/4 = 1/4^2 =
Question 90758This question is from textbook Beginning Al
: Solve by completing the square: 4x^2 + 2x - 3 = 0
4x^2 + 2x = 3
x^2 + 2/4x = 3/4
Square one-half of the of the x-coefficient and then add it to both sides
1/2 of 2/4 = 1/4^2 = 1/16
x^2 + 2/4x + 1/16 = 3/4 + 1/16
(x-1/4)^2 = 13/16
x - 1/4 = +/- radical 13 over radical 16
x - 1/4 = +/- radical 13 over 4
x = 1/4 +/- radical 13 over 4
x = 1 +/- radical 13 over 4 This question is from textbook Beginning Al
You can put this solution on YOUR website! A few minor errors in your work. The procedures you used were correct.
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4x^2 + 2x - 3 = 0 <=== ok
4x^2 + 2x = 3 <=== ok
x^2 + 2/4x = 3/4 <=== good!
Square one-half of the of the x-coefficient and then add it to both sides
1/2 of 2/4 = 1/4^2 = 1/16 <=== ok
x^2 + 2/4x + 1/16 = 3/4 + 1/16 <=== ok
(x-1/4)^2 = 13/16 <=== minor error. In the parentheses the sign is + not - because the
sign of the 2/4x term is + not minus.
x - 1/4 = +/- radical 13 over radical 16 <=== left side should be x + 1/4
x - 1/4 = +/- radical 13 over 4 <=== same. left side should be x + 1/4
x = 1/4 +/- radical 13 over 4 <===the right side should be -1/4 +/- (radical 13)/4
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This is the answer. If you want to write it as you did below you should use parentheses
to indicate that both terms are divided by 4.
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x = 1 +/- radical 13 over 4 should be x = (-1 +/- radical 13)/4
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This will indicate that your answer is:
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The way you originally wrote it implies that only the radical 13 is divided by 4 and that
the 1 is not. It becomes much clearer what you meant if you put the entire quantity
that is to be divided by 4 inside a set of parentheses.
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The most critical thing about your method is that you show an understanding of what you
are doing. A lot of students forget to divide to make the multiplier of the squared term
become 1. Moving the constant to the right side early in the problem is not necessary
but I like that you did it early in the problem. I always thought that it eliminated
a lot of chances for error. And you correctly divided the multiplier of the x term by 2
and squared it to find how much to add to each side of the equation. Good job! The only
check you need to make is when you write the squared term (in this problem it you wrote
(x -1/4)^2, the constant term (1/4) should be the same as you get when you divide the
multiplier of x (+2/4) by 2. In other words, when you divided the +2/4 by 2 you should have
gotten +1/4 and that would be the term that appears inside the parentheses.
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Hope this helps. Keep up the good work you are doing!!!
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