Mil.navy.01 completing the square

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In summary, completing the square in the Mil.navy.01 equation allows for the simplification and solving of quadratic equations. This is achieved by rearranging the equation, adding a constant term, and factoring it into a binomial. This method is only applicable to quadratic equations and is significant in creating a standard form and finding the minimum/maximum value. Other methods, such as factoring, the quadratic formula, and graphing, can also be used to solve quadratic equations, but completing the square is a useful alternative for more complex equations.
  • #1

karush

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$\tiny{mil.navy.01}$
This is on an sample entrance exam test for the Navy Academy

Use "completing the square" to rewrite
$x^2-4x+3=0$ in the form $\quad (x-c)^2=d$
a, $(x-1)^2=1$
b. $(x-2)^2=1$
c. $(x-3)^2=1$
d. $(x-2)^2=2$
e. $(x-4)^2=1$

ok I am not sure why they suggest the second transformation
 
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  • #2
\(\displaystyle x^2-4x+3 = 0\\
(x-2)^2 -4 + 3 = 0\\
(x-2)^2 = 1\)

I don't think the problem is suggesting anything.
Those are multiple choice answers only one of which is correct.
 
  • #3
$x^2-4x+3=0$
isolate
$x^2-4x=-3$
add 4 to both sides
$x^2-4x+4=-3+4$
simplify
$(x-2)^2=1$
 

1. What is the purpose of completing the square in "Mil.navy.01"?

The purpose of completing the square in "Mil.navy.01" is to convert a quadratic equation into its standard form, which makes it easier to solve and graph.

2. How do you complete the square in "Mil.navy.01"?

To complete the square in "Mil.navy.01", follow these steps:
1. Make sure the equation is in the form ax^2 + bx + c = 0
2. Divide both sides by a, if necessary
3. Move the constant term (c) to the right side of the equation
4. Take half of the coefficient of the x-term (b) and square it
5. Add this value to both sides of the equation
6. Factor the left side of the equation
7. Take the square root of both sides
8. Solve for x
The resulting equation will be in the form (x + b/2)^2 = (c-b^2/4a), which is the completed square form.

3. Why is completing the square important in "Mil.navy.01"?

Completing the square in "Mil.navy.01" is important because it allows us to easily find the vertex of a parabola, which is the highest or lowest point on the graph. It also helps us to solve quadratic equations and find the roots of the equation.

4. Can completing the square be used for any type of equation in "Mil.navy.01"?

Completing the square can only be used for quadratic equations in "Mil.navy.01", which are equations in the form ax^2 + bx + c = 0. It cannot be used for linear or cubic equations.

5. Are there any shortcuts or tricks for completing the square in "Mil.navy.01"?

There are a few shortcuts or tricks that can be used to complete the square in "Mil.navy.01". One is to remember the formula (x + b/2)^2 = (c-b^2/4a), which is the completed square form. Another trick is to use the pattern (x + b)^2 = x^2 + 2bx + b^2, and then adjust the constant term accordingly. Practice and familiarity with the process can also make completing the square easier and quicker.

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