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Simplifying 3y4 + -3y3 = 10y2 Reorder the terms: -3y3 + 3y4 = 10y2 Solving -3y3 + 3y4 = 10y2 Solving for variable 'y'. Reorder the terms: -10y2 + -3y3 + 3y4 = 10y2 + -10y2 Combine like terms: 10y2 + -10y2 = 0 -10y2 + -3y3 + 3y4 = 0 Factor out the Greatest Common Factor (GCF), 'y2'. y2(-10 + -3y + 3y2) = 0Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(-10 + -3y + 3y2)' equal to zero and attempt to solve: Simplifying -10 + -3y + 3y2 = 0 Solving -10 + -3y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -1y + y2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -1y + 3.333333333 + y2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -1y + y2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -1y + y2 = 0 + 3.333333333 -1y + y2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -1y + y2 = 3.333333333 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 3.333333333 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 3.333333333 + 0.25 Combine like terms: 3.333333333 + 0.25 = 3.583333333 0.25 + -1y + y2 = 3.583333333 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (y + -0.5) equal to 1.892969449 and -1.892969449.Subproblem 1
y + -0.5 = 1.892969449 Simplifying y + -0.5 = 1.892969449 Reorder the terms: -0.5 + y = 1.892969449 Solving -0.5 + y = 1.892969449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 1.892969449 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.892969449 + 0.5 y = 1.892969449 + 0.5 Combine like terms: 1.892969449 + 0.5 = 2.392969449 y = 2.392969449 Simplifying y = 2.392969449Subproblem 2
y + -0.5 = -1.892969449 Simplifying y + -0.5 = -1.892969449 Reorder the terms: -0.5 + y = -1.892969449 Solving -0.5 + y = -1.892969449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -1.892969449 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.892969449 + 0.5 y = -1.892969449 + 0.5 Combine like terms: -1.892969449 + 0.5 = -1.392969449 y = -1.392969449 Simplifying y = -1.392969449Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.392969449, -1.392969449}Solution
y = {0, 2.392969449, -1.392969449}
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