Question #8950d

2 Answers
Jun 23, 2017

#y=(x-2.5)^2+94.75#

Explanation:

#y=x^2-5x+101#

To complete the square, your goal is to make a perfect trinomial. For example:

#x^2+2x+1=(x+1)^2#

To make things easier, let's add some parentheses to the equation.

#y=(x^2-5x)+101#

You need to add a constant into the parentheses to create a perfect trinomial. To find this constant, use this formula:

#(b/2)^2#

The #b# comes from the standard form of a quadratic equation #y=ax^2+bx+c#. In this case, that means your #b# is #-5#.

#(-5/2)^2#

#(-2.5)^2#

#6.25#

This is where things can get a little confusing. Because you are adding a number on one side of the equation, and not the other side, you need to balance it out on the same side.

#y=(x^2-5x+6.25)+101-6.25#

As you can see, you've created your perfect trinomial while also not unbalancing your equation. Now you can factor and simplify!

#y=(x-2.5)^2+101-6.25#

#y=(x-2.5)^2+94.75#

Jun 23, 2017

#y = (x-5/2)^2+379/4 #

Explanation:

#x^2-5x+101#

To complete the square, we need to find a value that makes #x^2-5x# a perfect square. To make it easier to visualize, I like to move the other component (#101#) to the other side of the equation.

#-101=x^2-5x#

To solve for the missing component, we need to follow these steps:

1) take the middle term, #-5# and divide by #2#

#(-5)/2=-5/2#

2) square this solution

#(-5/2)^2 = 25/4#

Now, let's add this to the equation. REMEMBER in an equation, we can add whatever we want, but we must also add it to the other side:

#-101 + 25/4 = x^2-5x+25/4#

#-379/4 = (x-5/2)^2#

#(x-5/2)^2+379/4 #

Now we have our solution!

#y = (x-5/2)^2+379/4 #