Mathematics, 12.12.2019 21:31 littlequeenashley

Use the method of completing the square to transform the quadratic equation into the equation form (x + p)2 = q.

4x2 + 2x + 4 = 0
a) (x + 1/4)^2 = 15/16
b) (x + 1/2)^2 = 15/16
c) (x + 1/4)^2 = -15/16
d) (x + 1/2)^2 = -15/16

Answers: 3

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divide both sides of the equation by 2 to get:

(x + 1/4)^2 = -7/16 this is your solution.

continue further to solve for x if you care to, but the problem did not require you to do this.

take the square root of both sides of the equation to get:

x + 1/4 = plus or minus sqrt(-7/16)

subtract 1/4 from both sides of the equation to get x = -1/4 plus or minus sqrt(-7/16).

since sqrt(-7/16) is the same as sqrt(7/16) * i, your solution becomes:

x = -1/4 plus or minus sqrt(7/16) * i.

your problem was to convert it to the form of (x + p)2 = q.

the solution to that is:

(x + 1/4)^2 = -7/16 subtract 1 from both sides of the equation to get:

2x^2 + x = -1

factor out a 2 on the left side of the equation to get:

2 * (x^2 + x/2) = -1

complete the squares on x^2 + x/2 to get:

2 * ((x+1/4)^2 - (1/16)) = -1

simplify by distibuting the multiplication to get:

2 * (x+1/4)^2 - 2*(1/16) = -1

simplify further to get:

2 * (x+1/4)^2 - 1/8 = -1

add 1/8 to both sides of the equation to get:

2 * (x + 1/4)^2 = -7/8 .

Answer from: Quest

in english this is

ex.15 pag.85 create. write in ten lines the continuation of the ballad of the five motanasi, using verbs to the imperfect and to the perfect compound. five stars

hope i with whatever it is that you need! : )

Answer from: Quest

the speed is $135$ miles per hour > is false

step-by-step explanation:

we know that

a relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

in a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

the graph shown in the figure represent a direct variation

the slope of the line represent the speed

$y/x=k$

for the point $(1.5,90)$

substitute the values of x and y

$k=90/1.5=60\ miles/hour$

the linear equation is equal to

$y=60x$

statements

case a) it takes $2$ hours to go $120$ miles

the statement is true

because

substitute

for $x=2$

find the value of y in the linear equation

$y=60(2)=120\ miles$ > is correct

case b) the speed is $135$ miles per hour

the statement is false

because the speed is $60\ miles/hour$

case c) the unit rate for the trip is $60\ miles/hour$

the statement is true

because the speed is equal to the slope of the linear equation

case d) it took $20$ minutes to go the first $20$ miles

the statement is true

because

substitute

for $x=20\ minutes=(1/3)\ hour$

find the value of y in the linear equation

$y=60(1/3)=20\ miles$ > is correct

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