(8y 3+ 4y2 + 16y) ÷ 4y
Answers
Answer
y = {0}
Step-by-step explanation:
Simplifying
8y3 + -4y2 + 10y = 0
Reorder the terms:
10y + -4y2 + 8y3 = 0
Solving
10y + -4y2 + 8y3 = 0
Solving for variable 'y'.
Factor out the Greatest Common Factor (GCF), '2y'.
2y(5 + -2y + 4y2) = 0
Ignore the factor 2.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:
Simplifying
y = 0
Solving
y = 0
Move all terms containing y to the left, all other terms to the right.
Simplifying
y = 0
Subproblem 2
Set the factor '(5 + -2y + 4y2)' equal to zero and attempt to solve:
Simplifying
5 + -2y + 4y2 = 0
Solving
5 + -2y + 4y2 = 0
Begin completing the square. Divide all terms by
4 the coefficient of the squared term:
Divide each side by '4'.
1.25 + -0.5y + y2 = 0
Move the constant term to the right:
Add '-1.25' to each side of the equation.
1.25 + -0.5y + -1.25 + y2 = 0 + -1.25
Reorder the terms:
1.25 + -1.25 + -0.5y + y2 = 0 + -1.25
Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -0.5y + y2 = 0 + -1.25
-0.5y + y2 = 0 + -1.25
Combine like terms: 0 + -1.25 = -1.25
-0.5y + y2 = -1.25
The y term is -0.5y. Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.
Add '0.0625' to each side of the equation.
-0.5y + 0.0625 + y2 = -1.25 + 0.0625
Reorder the terms:
0.0625 + -0.5y + y2 = -1.25 + 0.0625
Combine like terms: -1.25 + 0.0625 = -1.1875
0.0625 + -0.5y + y2 = -1.1875
Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = -1.1875
Can't calculate square root of the right side.
The solution to this equation could not be determined.
This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}
Step-by-step explanation:
8y³ - 16y²
2y³ - 2y² - 4y (8y²-16y)
(2y² - 2y - 4) Now how about those 2 factors?
(4y²-8y) 2 (y²-y-2)
And any canceling? Yup.
4y (2) (y2) (y + 1)
4y
= y + 1