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4 years ago

What number should be added to both sides of the equation to complete the square x^2+8x=4

2 answers:

5 0

It would be half of the coefficient of x squared added to both sides:
So half of 8 ( the coefficient of 8x) is 4;
The number 4 squared is 16, so you would add that to both sides.

You do this so that you can easily factor the left side: x^2 + 8x + 16 = 4 + 16
(x + 4)(x+4) = 20

UkoKoshka [18]4 years ago

5 0

Answer:

To complete the square you have to add 20.

Step-by-step explanation:

The concept of square of a binomial can be represented as

(a + b)² = a² + b² + 2ab

Then given x² + 8x = 4 ⇒ x² + 8x -4 = 0. From this expression we can easy identify "a" as x. Then b can be obtained if we think that 2ab=8x

⇒2xb=8x ⇒b = 8x/2x ⇒b=4.

As you can see if a=x and b=4, then you have (x + 4)²

⇒(x + 4)²= x² + 16 + 8x.

Finally if the final expression is x² + 16 + 8x, you have to add 20 to the given expression.

x² + 8x - 4 + 20 = x² + 8x + 16.

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Luden [163]

Cone details:

height: h cm

radius: r cm

Sphere details:

radius: 10 cm

================

From the endpoints (EO, UO) of the circle to the center of the circle (O), the radius is will be always the same.

Using Pythagoras Theorem

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TO² + TU² = OU²

(h-10)² + r² = 10² [insert values]

r² = 10² - (h-10)² [change sides]

r² = 100 - (h² -20h + 100) [expand]

r² = 100 - h² + 20h -100 [simplify]

r² = 20h - h² [shown]

r = √20h - h² ["r" in terms of "h"]

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===========================

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (\sqrt{20h - h^2})^2 \ ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20h - h^2) (h)$

$\longrightarrow \sf V = \dfrac{1}{3} * \pi * (20 - h) (h) ( h)$

$\longrightarrow \sf V = \dfrac{1}{3} \pi h^2(20-h)$

To find maximum/minimum, we have to find first derivative.

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$\Longrightarrow \sf V' =\dfrac{d}{dx} ( \dfrac{1}{3} \pi h^2(20-h) )$

apply chain rule

$\sf \Longrightarrow V'=\dfrac{\pi \left(40h-3h^2\right)}{3}$

Equate the first derivative to zero, that is V'(x) = 0

$\Longrightarrow \sf \dfrac{\pi \left(40h-3h^2\right)}{3}=0$

$\Longrightarrow \sf 40h-3h^2=0$

$\Longrightarrow \sf h(40-3h)=0$

$\Longrightarrow \sf h=0, \ 40-3h=0$

$\Longrightarrow \sf h=0,\:h=\dfrac{40}{3}$

maximum volume: when h = 40/3

$\sf \Longrightarrow max= \dfrac{1}{3} \pi (\dfrac{40}{3} )^2(20-\dfrac{40}{3} )$

$\sf \Longrightarrow maximum= 1241.123 \ cm^3$

minimum volume: when h = 0

$\sf \Longrightarrow min= \dfrac{1}{3} \pi (0)^2(20-0)$

$\sf \Longrightarrow minimum=0 \ cm^3$

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What number should be added to both sides of the equation to complete the square x^2+8x=4​

What number should be added to both sides of the equation to complete the square x^2+8x=4