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Simplifying (-2y2 + -9y) + (4y2 + y + -2) = 0 Reorder the terms: (-9y + -2y2) + (4y2 + y + -2) = 0 Remove parenthesis around (-9y + -2y2) -9y + -2y2 + (4y2 + y + -2) = 0 Reorder the terms: -9y + -2y2 + (-2 + y + 4y2) = 0 Remove parenthesis around (-2 + y + 4y2) -9y + -2y2 + -2 + y + 4y2 = 0 Reorder the terms: -2 + -9y + y + -2y2 + 4y2 = 0 Combine like terms: -9y + y = -8y -2 + -8y + -2y2 + 4y2 = 0 Combine like terms: -2y2 + 4y2 = 2y2 -2 + -8y + 2y2 = 0 Solving -2 + -8y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -4y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4y + y2)' equal to zero and attempt to solve: Simplifying -1 + -4y + y2 = 0 Solving -1 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -4y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -4y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4y + y2 = 0 + 1 -4y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -4y + y2 = 1 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 = 1 + 4 Reorder the terms: 4 + -4y + y2 = 1 + 4 Combine like terms: 1 + 4 = 5 4 + -4y + y2 = 5 Factor a perfect square on the left side: (y + -2)(y + -2) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (y + -2) equal to 2.236067978 and -2.236067978.Subproblem 1
y + -2 = 2.236067978 Simplifying y + -2 = 2.236067978 Reorder the terms: -2 + y = 2.236067978 Solving -2 + y = 2.236067978 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 = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + y = 2.236067978 + 2 y = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 y = 4.236067978 Simplifying y = 4.236067978Subproblem 2
y + -2 = -2.236067978 Simplifying y + -2 = -2.236067978 Reorder the terms: -2 + y = -2.236067978 Solving -2 + y = -2.236067978 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 = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + y = -2.236067978 + 2 y = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 y = -0.236067978 Simplifying y = -0.236067978Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.236067978, -0.236067978}Solution
y = {4.236067978, -0.236067978}
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