SOLUTION: For the equation x-2sqrtx=0 , perform the following: a) Solve for all values of x that satisfies the equation. Answer: Show work in this space. b) Graph the func

Question 77193: For the equation x-2sqrtx=0 , perform the following:
a) Solve for all values of x that satisfies the equation.
Answer:
Show work in this space.

b) Graph the functions y = x and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
Graph:

Points of intersection:

Found 2 solutions by stanbon, bucky:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
For the equation x-2sqrtx=0 , perform the following:
a) Solve for all values of x that satisfies the equation.
Answer:
Show work in this space.
2sqrtx=x
Square both sides after dividing both sides by 2 to get:
x=(x/2)^2
x=x^2/4
x^2-4x=0
x(x-4)=0
x=0 or x=4
============
b) Graph the functions y = x and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
Graph:
Points of intersection:
You did not post both of the functions.
The one you did post is a line thru (0,0), (1,1)
============
Cheers,
Stan H.

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
First part of the problem:
.
Given:
.

.
Find all the values of x that satisfy this equation.
.
The method involves getting the radical term on one side of the equation and the other term
on the other side. We can do this by adding to both sides and the equation
then becomes:
.

.
Next square both sides. Note that when you do that, the right side squares as follows:
.

.
and the equation therefore squares to:
.

.
Subtract 4x from both sides and the equation is then:
.

.
Factor the common "x" from both terms on the left side to get:
.

.
Note that this equation will be true if either of the factors is zero. Therefore,
one at a time we can set the factors equal to zero to solve the equation. First:
.

.
That is one answer. Then:
.

.
Solve by adding 4 to both sides to get:
.

.
So the answer to the first part of this problem is that the equation given in the problem
will be satisfied by two values of x ... x = 0 and x = 4.
.
For the second part of the problem the two graphs should look like this:
.

.
Note that the original equation given in the problem does not permit x to be less than
zero because for real values you are not permitted to take the square root of a negative
number.
.
The red line is the graph of and the green line is the graph of
.
Note that the green line is on the x-axis at the two values of x that we found previously,
x = 0 and x = +4. Also note that the only place the two equations intersect is at the
origin. You can also show this is true mathematically by solving the equation set:
.
and
.
Solve by substitution. The first equation tells us that y equals x so we can substitute
x for y in the second equation. With this substitution, the second equation becomes:
.

.
Subtract x from both sides and the equation reduces to:
.

.
Square both sides and you get:
.

.
and divide both sides by 4 to find that:
.

.
Then you can solve for the corresponding value of y by returning to the equation
and plugging in 0 for x to find that y also = 0. The only common point on the two graphs
is (0,0) ... the origin as is shown on the graphs themselves.
.
Hope this helps you to understand the problem and how to go about getting the solution
to it.
.

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