Can someone show me the steps to solve this problems..
18s^2 + 72s = 0
and
x^3 - 5x^2 - 66x = 0
18s^2 + 72s = 0
18s*(s + 4)=0
set both terms equal to zero.
x^3 - 5x^2 - 66x = 0
x*(x^2 - 5x - 66 )= 0
factor the second term (11,6)
Sure! Here are the steps to solve the given problems:
Problem 1: 18s^2 + 72s = 0
Step 1: Notice that both terms in the equation have a common factor of 18s. So, we can rewrite the equation as 18s(s + 4) = 0.
Step 2: Now, set each factor equal to zero:
18s = 0
This implies s = 0.
s + 4 = 0
Subtract 4 from both sides, we get s = -4.
Therefore, the solutions to the equation 18s^2 + 72s = 0 are s = 0 and s = -4.
Problem 2: x^3 - 5x^2 - 66x = 0
Step 1: Notice that the equation can be factored by grouping. Factor out the common factor of x:
x(x^2 - 5x - 66) = 0.
Step 2: Now, we need to factor the quadratic term, x^2 - 5x - 66. We can use the quadratic factoring method or quadratic formula to find its roots. Let's use the factoring method here.
The quadratic term can be factored as (x - 11)(x + 6).
Therefore, the factored equation becomes:
x(x - 11)(x + 6) = 0.
Now, set each factor equal to zero:
x = 0,
x - 11 = 0 (solve for x),
x + 6 = 0 (solve for x).
The solutions to the equation x^3 - 5x^2 - 66x = 0 are x = 0, x = 11, and x = -6.