completing the square solving quadratics by completing the square must be a perfect square
DESCRIPTION
Perfect Square On One side Take Square Root of BOTH SIDES But what happens if you DON’T have a perfect square on one side……. You make it a Perfect Square Use the relations on next slide…TRANSCRIPT
Completing the Square
Solving Quadratics By
Completing the SquareMust be a perfectSquare
2( 5) 64x 5 8x
When you take the square root, You MUST consider the Positive and Negative answers.
5 8x 5 8x 5 5
13x 5 5
3x
PerfectSquare
On One side
Take Square Root
ofBOTH SIDES
2 ( 5) 64x
PerfectSquare
On One side
Take Square Root
ofBOTH SIDES
But what happens if you DON’T have a perfect square on one side…….
You make it a Perfect Square
Use the relations on next slide…
2( 6)x ( 2 ) To expand a perfect square binomial:
2 12 36x x 6x 26
We can use these relations to find the missing term….To make it a perfect square trinomial that can be factored into a perfect square binomial.
2 _ _12 _x x 12 2 6 626 36
36
2x
Take ½ middle term
Then square it
The resulting trinomial is called a perfect square trinomial,
which can be factored into a perfect square binomial.
2 _ _18 _ _x x
18 2 92(9) 81
81 2( 9)x
1. 2 12 0x x
1. Make one side a perfect square
2. Add a blank to both sides
3. Divide “b” by 2
4. Square that answer.
5. Add it to both sides
6. Factor 1st side
7. Square root both sides
8. Solve for x
2 0x x ___ ___ 12 2 6
2(6) 36
36 362( 6)x 362( 6) 36x 6 6x
6 6x 6 6x 6 6
12x 6 6
0x
12
Factor this Perfect square trinomial2 12 36x x
What is the
Square root
of x2
2( )x
Bring dow
n sign
6W
hat is the S
quare root of 36
2( 6)x
2. 2 8 0x x
1. Move constant to other side.
2. Add a blank to both sides
3. Divide “b” by 2
4. Square that answer.
5. Add it to both sides
6. Factor 1st side
7. Square root both sides
8. Solve for x
2 8x x ___ ___6 2 3
2(3) 9
9 92( 3)x 12( 3) 1x
3 1x 3 1x 3 1x 3 3
4x 3 3
2x
6
6
Factor this Perfect square trinomial2 6 9x x
What is the
Square root
of x2
2( )x
Bring dow
n sign
3W
hat is the S
quare root of 9
2( 3)x
3. 2 8 84 0x x
1. Move constant to other side.
2. Add a blank to both sides
3. Divide “b” by 2
4. Square that answer.
5. Add it to both sides
6. Factor 1st side
7. Square root both sides
8. Solve for x
2 84x x ___ ___8 2 4
2(4) 1616 16
2( 4)x 1002( 4) 100x
4 10x 4 10x 4 10x 4 4
14x 4 4
6x
8
Factor this Perfect square trinomial2 8 16x x
What is the
Square root
of x2
2( )x
Bring dow
n sign
4W
hat is the S
quare root of 9
2( 4)x
4. 2 2 15 0x x
1. Move constant to other side.
2. Add a blank to both sides
3. Divide “b” by 2
4. Square that answer.
5. Add it to both sides
6. Factor 1st side
7. Square root both sides
8. Solve for x
2 15x x ___ ___2 2 1
2(1) 11 1
2( 1)x 162( 1) 16x
1 4x 1 4x 1 4x 1 1
3x 1 1
5x
2
Factor this Perfect square trinomial2 2 1x x
What is the
Square root
of x2
2( )x
Bring dow
n sign
1W
hat is the S
quare root of 9
2( 1)x
Steps to solve Quadratics by completing the square:
Move the constant to side by itself. Make the side (w/variables) a perfect square by
adding a certain number to both sides. To calculate this number
– Divide “b” (middle term) by 2– Then square that answer
Take the square root of both sides of eq Then solve for x
In a perfect square, there is a relationship between the coefficient of the middle term and the constant term.
2( 7)x
7 1 (14)2
27 49
2 14 49x x
7