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3 years ago

What value should be added to the expression to create a perfect square? x^2 - 20x

1 answer:

4 0

To complete the square:
we take the coefficient ox "x" (which in this problem is -20)
we divide it by 2
square that number
then add it to both sides of the equation

-20 / 2 = -10
-10^2 = 100
then we add 100 to both sides of the equation:
x^2 -20x
x^2 -20x +100 = 100
******************************************************
To get the roots of the equation, we take the square root of both sides:
(x -10) * (x-10) = 10
(x-10) = square root (10)
x-10 = 3.1622776602 
x1 = 13.1622776602 
and don't forget that square root of 10 also equals -3.1622776602 
x2 = 10 - 3.1622776602
x2 = 6.8377223398

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Answer:

A. $y=3x-10$

C. $y+6=3(x-15)$

Step-by-step explanation:

Given:

The given line is $6x+18y=5$

Express this in slope-intercept form $y=mx+b$ , where m is the slope and b is the y-intercept.

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Therefore, the slope of the line is $m=-\frac{1}{3}$ .

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Let us find the slopes of each lines.

Option A:

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On comparing with the slope-intercept form, we get slope as $m_{A}=3$ .

Now, $m\times m_{A}=-\frac{1}{3}\times 3=-1$ . So, option A is perpendicular to the given line.

Option B:

For lines of the form $x=a$ , where, a is a constant, the slope is undefined. So, option B is incorrect.

Option C:

On comparing with the slope-point form, we get slope as $m_{C}=3$ .

Now, $m\times m_{C}=-\frac{1}{3}\times 3=-1$ . So, option C is perpendicular to the given line.

Option D:

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On comparing with the slope-intercept form, we get slope as $m_{D}=-\frac{1}{3}$ .

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3 years ago

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