Rational Completeing the Square

• ISX
In summary, the conversation discusses a problem with multiplying fractions in a mathematical equation. The individual is struggling to understand why their solution is not matching up with the given solution, and realizes that they have been incorrectly squaring fractions. They thank the others for their help and acknowledge their mistake.
ISX

The Attempt at a Solution

Alright so the solution is in the above pic, but I can't get anywhere close. You can see from the green circles that the "squares" aren't matching up. So I'm not sure if I can't multiply fractions anymore or what.

ISX said:

Homework Statement

[ IMG]http://i49.tinypic.com/51v52u.jpg[/PLAIN]

Homework Equations

[ IMG]http://i50.tinypic.com/9fxswl.jpg[/PLAIN]

The Attempt at a Solution

Alright so the solution is in the above pic, but I can't get anywhere close. You can see from the green circles that the "squares" aren't matching up. So I'm not sure if I can't multiply fractions anymore or what.
[ IMG]http://i47.tinypic.com/2ivzmoj.jpg[/PLAIN]

$\displaystyle x^2-\frac{5}{6}x+\frac{25}{144}=-\frac{1}{6}+\frac{25}{144}$

is correct.

What your last line shows (correctly) is that $\displaystyle \left(x-\frac{5}{6}\right)^2\ne x^2-\frac{5}{6}x+\frac{25}{144}\ .$

When you square 5/6, you don't get 25/144 .

How did you get 25/144 in the first place? You squared 5/12 not 5/6 .

Attachments

• 2ivzmoj.jpg
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you went from
$x^2 +bx + (\frac{b}{2})^{2}$
to
$(x+b)^{2}$

and not to

$(x+\frac{b}{2})^{2}$

Hellllllll I've been doing it wrong for centuries then. Let's try this again.

Ahhhh! Thanks for the help guys! I was always just dropping the last number off and went with the first 2. Guess I never caught on that fractions didnt work that way.

1. What is the purpose of completing the square?

The main purpose of completing the square is to convert a quadratic equation into a perfect square trinomial. This makes it easier to solve the equation and find the solutions for the variable.

2. How do you complete the square?

To complete the square, you need to follow a specific set of steps. First, make sure the coefficient of the squared term is 1. Then, take half of the coefficient of the x-term and square it. Add this value to both sides of the equation. Finally, factor the perfect square trinomial and take the square root of both sides to solve for the variable.

3. When should I use completing the square?

Completing the square is typically used when solving quadratic equations that cannot be easily factored or when the quadratic equation has a leading coefficient other than 1. It can also be used to find the minimum or maximum value of a quadratic function.

4. What are the benefits of completing the square?

Completing the square allows you to solve quadratic equations that cannot be factored using other methods. It also helps in graphing quadratic equations and finding key points such as the vertex, axis of symmetry, and x-intercepts.

5. Are there any drawbacks to completing the square?

One potential drawback of completing the square is that it can be a time-consuming process. It also requires a good understanding of algebraic manipulation and may not always result in rational solutions. In some cases, other methods such as using the quadratic formula may be quicker and more efficient.

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