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Equation
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x² + 4x = 0
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Add a constant
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x² + 4x + (4/2)² - (4/2)² = 0 ← Add 2² to form perfect square
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Evaluate bracket
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x² + 4x + 2² - 2² = 0
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Form the perfect square
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(x + 2)² = 4
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Square root both sides
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(x+2) =
√4
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Evaluate the square root
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(x+2) = 2
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Solve x
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x = 2 - 2 or x = -2 - 2
x = 0 or -4
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Answer: The constant to add is 4 and the value of x = 0 or -4
------------------------------------------------------------------
Equation
------------------------------------------------------------------
x² + 4x = 0
------------------------------------------------------------------
Add a constant
------------------------------------------------------------------
x² + 4x + (4/2)² - (4/2)² = 0 ← Add 2² to form perfect square
------------------------------------------------------------------
Evaluate bracket
------------------------------------------------------------------
x² + 4x + 2² - 2² = 0
------------------------------------------------------------------
Form the perfect square
------------------------------------------------------------------
(x + 2)² = 4
------------------------------------------------------------------
Square root both sides
------------------------------------------------------------------
(x+2) =
------------------------------------------------------------------
Evaluate the square root
------------------------------------------------------------------
(x+2) =
------------------------------------------------------------------
Solve x
------------------------------------------------------------------
x = 2 - 2 or x = -2 - 2
x = 0 or -4
------------------------------------------------------------------
Answer: The constant to add is 4 and the value of x = 0 or -4
------------------------------------------------------------------
Since the photo booth charges a $500 fee for two hours at the party and an additional 50 dollars per hour, we have:
50x+500=C
Where x is the hours stayed and C is the total cost. Since Cindy doesn't want to spend more than 700 dollars, we have:
So she spent an additional 4 hours on the rental.