X^2-2x=0 solve by completing the square

2 answers:

6 0

X^2 -2x = 0
Get the coefficient of x
divide it by 2
square it
add it to both sides
-2 / 2 = -1
-1^2 = 1
x^2 -2x +1= 1
Take the square root of both sides
(x-1) = sq root (1)

Oksi-84 [34.3K]3 years ago

5 0

First, halve the second coefficient (-2) and then square it:
-2/2 = -1, (-1)^2 = 1, then add it to both sides:
$x^{2} -2x +1 = 1$
Now on the left side, we can rewrite this as:
$x^{2} - x - x + 1 = 1$
Factor out an x from the first two terms:
$x(x-1) - x + 1 = 1$
Factor out a -1 from the last two terms:
$x(x-1) - 1(x-1) = 1$
Now we can rewrite it as:
$(x-1)(x-1) = 1$
Which is equal to:
$(x-1)^{2} = 1$
Square root both sides, keeping in mind that leaves us with plus or minus one on the right:
$(x-1) = 1$
$(x-1) = -1$
Add one to both sides in both equations to solve for our two roots:
$x = 2, 0$

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A carpenter used 9 1/2 ft of cedar for every 7 2/3 ft of redwood for a construction project. If the carpenter uses 4 3/4 ft of c

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We can make a proportion to represent the woods used. On the top is cedar, and on the bottom is the redwood. On the left is what was used the first time, on the right is the current problem.

Before making the proportion, let's do a preliminary step and write all the fractions as improper fractions. We do this because we can't directly multiply or divide mixed numbers, but we can with fractions.

$9\frac{1}{2} = \frac{2 * 9 + 1}{2} =\frac{19}{2}$ <-- Multiply denominator times whole number and add the leftover fraction.

$7\frac{2}{3} = \frac{3 * 7 + 2}{3} =\frac{23}{3}$

$4\frac{3}{4} = \frac{4 * 4 + 3}{4} =\frac{19}{4}$

Now we set up the proportion. We solve it by cross multiplying.

$\frac{Cedar}{Redwood} =\frac{Cedar}{Redwood}$

$\frac{19/2}{23/3} =\frac{19/4}{R}$

$\frac{19}{2} R = \frac{23}{3} *\frac{19}{4}$

It may seem right to simplify the right side, but let's leave it alone. We divide both sides by 19/2.

$R = (\frac{23}{3} *\frac{19}{4} ) / \frac{19}{2}$

Dividing by a fraction means multiplying by its reciprocal. Thus,

$R = \frac{23}{3} *\frac{19}{4} * \frac{2}{19}$

Here's where not simplifying really pays off. We can simplify NOW and the terms go away more easily. The 19s go away and simplify to 1, and the 2 and 4 simplify to 1 and 2. All this happens by dividing out common numbers.

$R = \frac{23}{3} *\frac{1}{2} * \frac{1}{1}$