Start with your equation Move the # term to the other side, and leave a space Determine what HALF of...
3
x 2 + x 2 + 3 x 2 + x 2 + x + ( x + ( x ( x + x +3 x = Start with your equation Move the # term to the other side, and leave a space Determine what HALF of the coefficient of X is Factor the left side Write the left side as a single factor squared Take the square root of both sides Simplify each square root Set the left side equal to each answer from the right Solve each of the equations for X Combine like terms on the right side of the equation Square that number, and add it to both sides Completing the Square
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Transcript of Start with your equation Move the # term to the other side, and leave a space Determine what HALF of...
€
x 2 + 6x + 8 = 0
€
x 2 + 6x = −8
€
3
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x 2 + 6x + 9 = −8 + 9
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x 2 + 6x + 9 =1
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x + 3( ) x + 3( ) =1
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x + 3( )2
=1
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x + 3( )2
= ± 1
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x + 3 = ±1
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x + 3 =1 or x + 3 = −1
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x = −2 or x = −4
Start with your equation
Move the # term to the other side, and leave a space
Determine what HALF of the coefficient of X is
Factor the left side
Write the left side as a single factor squared
Take the square root of both sides
Simplify each square root
Set the left side equal to each answer from the right
Solve each of the equations for X
Combine like terms on the right side of the equation
Square that number, and add it to both sides
Completing the Square
Completing the Square
Start with your equation
Move the # term to the other side, and leave a space
Determine what HALF of the coefficient of X is
Factor the left side
Write the left side as a single factor squared
Take the square root of both sides
Simplify each square root
Set the left side equal to each answer from the right
Solve each of the equations for X
Combine like terms on the right side of the equation
Square that number, and add it to both sides
€
x 2 − 8x − 33 = 0
€
x 2 − 8x = 33
€
− 4
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x 2 − 8x +16 = 33 +16
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x 2 − 8x +16 = 49
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x − 4( ) x − 4( ) = 49
€
x − 4( )2
= 49
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x − 4( )2
= ± 49
€
x − 4 = ±7
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x − 4 = 7 or x − 4 = −7
€
x =11 or x = −3
Completing the SquareStart with your equation
Move the # term to the other side, and leave a space
Determine what HALF of the coefficient of X is
Factor the left side
Write the left side as a single factor squared
Take the square root of both sides
Simplify each square root
Set the left side equal to each answer from the right
Solve each of the equations for X
Combine like terms on the right side of the equation
Square that number, and add it to both sides
€
x2 − 5x+ 6 = 0
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x2 − 5x = −6
€
−52
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x2 − 5x+254
= −6 +254
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x2 − 5x+254
=14
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x− 52( ) x− 5
2( ) =14
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x− 52( )
2
=14
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x− 52( )
2
= ±14
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x− 52 = ±
12
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x− 52 =
12or x− 5
2 = −12
€
x =62
= 3 or x =42
= 2
