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

1 answer:

7 0

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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) = $\pm$ √4

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Evaluate the square root
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(x+2) = $\pm$ 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
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Find the area of the shaded portion in each of the following

MrRa [10]

Answer:

30.5 cm^2

Step-by-step explanation:

<h3><u>General outline</u></h3>

Find the area of the full circle
Find the area of the rectangle
Find the difference (full circle area - rectangle area)

<h3><u>Step 1. Find the area of the full circle</u></h3>

Recall the formula for the area of a circle: $A_{circle}=\pi r^2$ where $\pi \approx 3.14$ , and "r" is the radius of the circle (distance from center to any point on the edge).

From the diagram, the radius is 5cm.

$A_{circle}=\pi r^2$

$A_{circle}=(3.14)(5[cm])^2$

$A_{circle}=78.5[cm^2]$

<h3><u>Step 2. Find the area of the rectangle</u></h3>

Recall the formula for the area of a rectangle: $A_{rectangle}=bh$ where "b" is the base of the rectangle (length of bottom or length of top), "h" is the height of the rectangle (distance from bottom to top).