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diamong [38]
3 years ago
8

What number would you add to the equation below to complete the square?x2 + 4x = 0?

Mathematics
1 answer:
julia-pushkina [17]3 years ago
7 0
------------------------------------------------------------------
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) = \pm √4

------------------------------------------------------------------
Evaluate the square root
------------------------------------------------------------------
(x+2) = \pm 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
------------------------------------------------------------------



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