Given 25x^2 - 10x = 0, which values of x will satisfy the equation? (Hint: Factor the polynomial into two terms, and find the values of x that will make each term 0.)
A. x = 0 and x = 5/2
B. x = 0 and x = 2/5
C. x = 0 and x = 2
D. x = 0 and x = 5
Improvement over your last post.
25x^2 - 10x = 0
5x(5x-2) = 0
5x = 0 ---> x=0
or
5x-2=0 ---> x = 5/2
x= 0
x = 2/5 not 5/2
Reiny is wrong
5x-2 = 0
5x= 2
x = 2/5
Obviously x = 0
25 x ^ 2 - 10 x = 0
25 * 0 ^ 2 - 10 * 0 = 0
25 * 0 - 10 * 0 = 0
0 - 0 = 0
0 = 0
and
25 x ^ 2 - 10 x = 0 Divide both sides by 5 x
25 x ^ 2 / 5 x - 10 x / 5 x = 0 / 5 x
5 * 5 * x * x / 5 x - 2 * 5 x / 5 x = 0
5 x - 2 = 0 Add 2 to both sides
5 x - 2 + 2 = 0 + 2
5 x = 2 Divide both sides by 5
5 x / 5 = 2 / 5
x = 2 / 5
B. x = 0 and x = 2 / 5
To find the values of x that will satisfy the equation 25x^2 - 10x = 0, we can factor the polynomial and solve for x.
Step 1: Factor out the greatest common factor from the expression.
In this case, the greatest common factor is 5x because both terms have a factor of 5x. So we can rewrite the equation as:
5x(5x - 2) = 0.
Step 2: Set each factor equal to zero and solve for x.
Setting 5x = 0, we find x = 0.
Setting 5x - 2 = 0, we can solve for x by adding 2 to both sides of the equation:
5x = 2
x = 2/5.
So the values of x that will satisfy the equation are x = 0 and x = 2/5.
Therefore, the correct answer is B. x = 0 and x = 2/5.