The answer is the third one: 32 inches
What number would you add to the equation below to complete the square?x2 + 4x = 0?
1 answer:
------------------------------------------------------------------
Equation
------------------------------------------------------------------
x² + 4x = 0
------------------------------------------------------------------
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
------------------------------------------------------------------
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
------------------------------------------------------------------
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<h2>Explanation:</h2><h3>Part A.</h3>
The boundary lines of both inequalities will be dashed, because neither includes the "or equal to" case.
The first inequality solution area is bounded by a line with slope +5 and y-intercept +5. The solution area is above the line (y is greater than ...). Since the line rises steeply, the solution area looks to be to the left of the line. (It is shaded red on the attached graph.)
The second inequality solution area is bounded by a line with slope -1/2 and y-intercept +1. The solution area for this inequality is also above the line.
The solution area is where the two solution spaces overlap, in the quadrant to the upper left of the point where the lines intersect.
___
<h3>Part B.</h3>The graph shows the point (-2, 5) to be in the solution space.
We can show this point satisfies both inequalities.
- 5 > 5(-2)+5 ⇒ 5 > -5 . . . true
- 5 > (-1/2)(-2) +1 ⇒ 5 > 2 . . . true