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Simplifying (4y3 + -3y) + -1(6y + 4y2 + 3y3) = 0 Reorder the terms: (-3y + 4y3) + -1(6y + 4y2 + 3y3) = 0 Remove parenthesis around (-3y + 4y3) -3y + 4y3 + -1(6y + 4y2 + 3y3) = 0 -3y + 4y3 + (6y * -1 + 4y2 * -1 + 3y3 * -1) = 0 -3y + 4y3 + (-6y + -4y2 + -3y3) = 0 Reorder the terms: -3y + -6y + -4y2 + 4y3 + -3y3 = 0 Combine like terms: -3y + -6y = -9y -9y + -4y2 + 4y3 + -3y3 = 0 Combine like terms: 4y3 + -3y3 = 1y3 -9y + -4y2 + 1y3 = 0 Solving -9y + -4y2 + 1y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-9 + -4y + y2) = 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 '(-9 + -4y + y2)' equal to zero and attempt to solve: Simplifying -9 + -4y + y2 = 0 Solving -9 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -4y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -4y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4y + y2 = 0 + 9 -4y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4y + y2 = 9 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 9 + 4 Reorder the terms: 4 + -4y + y2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + -4y + y2 = 13 Factor a perfect square on the left side: (y + -2)(y + -2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y + -2) equal to 3.605551275 and -3.605551275.Subproblem 1
y + -2 = 3.605551275 Simplifying y + -2 = 3.605551275 Reorder the terms: -2 + y = 3.605551275 Solving -2 + y = 3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + y = 3.605551275 + 2 y = 3.605551275 + 2 Combine like terms: 3.605551275 + 2 = 5.605551275 y = 5.605551275 Simplifying y = 5.605551275Subproblem 2
y + -2 = -3.605551275 Simplifying y + -2 = -3.605551275 Reorder the terms: -2 + y = -3.605551275 Solving -2 + y = -3.605551275 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -3.605551275 + 2 Combine like terms: -2 + 2 = 0 0 + y = -3.605551275 + 2 y = -3.605551275 + 2 Combine like terms: -3.605551275 + 2 = -1.605551275 y = -1.605551275 Simplifying y = -1.605551275Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.605551275, -1.605551275}Solution
y = {0, 5.605551275, -1.605551275}
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