Solving quadratic equations by completing the square - PowerPoint PPT Presentation

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Solving quadratic equations by completing the square

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Solving quadratic equations by completing the square Perfect Square Trinomials Perfect Square Trinomials Perfect Square Trinomials Completing the ... – PowerPoint PPT presentation

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Title: Solving quadratic equations by completing the square


1
Solving quadratic equations by completing the
square
2
Perfect Square Trinomials
Before we solve equations by completing the
square, we should be familiar with perfect square
trinomials. A perfect square trinomial is a
trinomial like
3
Perfect Square Trinomials
Lets observe the pattern.
The 1st term is a perfect square.
The last term is a perfect square.
Half of the middle term is the square root of the
1st term times the square root of the last term.
4
Perfect Square Trinomials
Other examples. Notice The last sign in the
trinomial is always positive The sign in the
parentheses matches the sign of the middle
term.
5
Completing the square
Completing the square is a way of artificially
creating a perfect square trinomial. Lets start
with an easy example
Move the constant to the other side. Leave a big
old hole. Fill the hole with (half of 6)2 or
9. You have to add 9 to both sides.
6
Completing the square
Now lets finish the problem.
Factoring our artfully constructed perfect
square. Taking the square root of each
side. Solving the 2 possible equations.
7
Medium hard problem
On to a harder problem.
Oops! The coefficient of x isnt even. We just
go ahead and follow the pattern Take half of 3
and square it.
8
Medium hard problem
Add to each side
Use LCD to add fractions
Take square root of each side.
9
Medium hard problem
Lets finish up!
10
Hard problem
When you complete the square, the coefficient of
the square term has to be 1. What to do? What
to do?? Divide everything by 2 thats what to
do!
11
Hard problem
Now we have Now we have to take half of the
coefficient of x and square it.
12
Hard problem
Were going to add to each side
Use LCD to add fractions
13
Hard problem
Take the square root of each side
14
Hard problem
Add to each side and get 2 answers
15
Completing the square
  • The coefficient of the squared term must be 1
  • Divide if necessary
  • Move the constant to the right of the
  • Take half of the coefficient of x and square it
  • Add that to both sides of the
  • Use the LCD to add or subtract fractions
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