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Simplifying 5y + 6y2 = 4y3 Solving 5y + 6y2 = 4y3 Solving for variable 'y'. Combine like terms: 4y3 + -4y3 = 0 5y + 6y2 + -4y3 = 0 Factor out the Greatest Common Factor (GCF), 'y'. y(5 + 6y + -4y2) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(5 + 6y + -4y2)' equal to zero and attempt to solve: Simplifying 5 + 6y + -4y2 = 0 Solving 5 + 6y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -1.5y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1.5y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1.5y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1.5y + y2 = 0 + 1.25 -1.5y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1.5y + y2 = 1.25 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = 1.25 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = 1.25 + 0.5625 Combine like terms: 1.25 + 0.5625 = 1.8125 0.5625 + -1.5y + y2 = 1.8125 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = 1.8125 Calculate the square root of the right side: 1.346291202 Break this problem into two subproblems by setting (y + -0.75) equal to 1.346291202 and -1.346291202.Subproblem 1
y + -0.75 = 1.346291202 Simplifying y + -0.75 = 1.346291202 Reorder the terms: -0.75 + y = 1.346291202 Solving -0.75 + y = 1.346291202 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = 1.346291202 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = 1.346291202 + 0.75 y = 1.346291202 + 0.75 Combine like terms: 1.346291202 + 0.75 = 2.096291202 y = 2.096291202 Simplifying y = 2.096291202Subproblem 2
y + -0.75 = -1.346291202 Simplifying y + -0.75 = -1.346291202 Reorder the terms: -0.75 + y = -1.346291202 Solving -0.75 + y = -1.346291202 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + y = -1.346291202 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + y = -1.346291202 + 0.75 y = -1.346291202 + 0.75 Combine like terms: -1.346291202 + 0.75 = -0.596291202 y = -0.596291202 Simplifying y = -0.596291202Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.096291202, -0.596291202}Solution
y = {0, 2.096291202, -0.596291202}
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