Objective To complete a square for a quadratic equation and solve by completing the square Steps to complete the square 1 You will get an expression that looks like this AX ² BX ID: 717277
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Slide1
2.4 Completing the Square
Objective: To complete a square for a quadratic equation and solve by completing the squareSlide2
Steps to complete the square
1.) You will get an expression that looks like this:
AX
²+ BX
2.) Our goal is to make a square such that we have
(a + b)² = a² +2ab + b²
3.) We take ½ of the X coefficient
(Divide the number in front of the X by 2)
4.) Then square that numberSlide3
To
Complete the Square
x
2
+ 6x
Take half of the coefficient of ‘x’ Square it and add it
3
9
x2 + 6x + 9
= (x + 3)
2Slide4
Complete the square, and show what the perfect square is:Slide5
To solve by completing the square
If a quadratic equation does not factor we can solve it by two different methods
1.) Completing the Square (today’s lesson)
2.) Quadratic Formula (Next week’s lesson)Slide6
Steps to solve by
completing
the square
1.) If the quadratic does not factor, move the
constant to the other side of the equation
Ex: x²-4x -7 =0 x²-4x=7
2.) Work with the x²+ x side of the equation and complete the square by taking ½ of the coefficient
of x and squaring Ex. x² -4x 4/2= 2²=4
3.) Add the number you got to complete the square to both sides of the equation Ex: x² -4x +4 = 7 +44.)Simplify your trinomial square
Ex: (x-2)² =11
5.)Take the square root of both sides of the equation
Ex: x-2 =±√11
6.) Solve for x
Ex: x=2±√11Slide7
Solve by
Completing the Square
+9
+9Slide8
Solve by
Completing the Square
+121
+121Slide9
Solve by
Completing the Square
+1
+1Slide10
Solve by
Completing the Square
+25
+25Slide11
Solve by
Completing the Square
+16
+16Slide12
Solve by
Completing the Square
+9
+9Slide13
The coefficient of x
2
must be “1”Slide14
The coefficient of x
2
must be “1”Slide15