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Simplifying (-4y2 + 5y + -2) + (3y2 + 6y + 1) = 0 Reorder the terms: (-2 + 5y + -4y2) + (3y2 + 6y + 1) = 0 Remove parenthesis around (-2 + 5y + -4y2) -2 + 5y + -4y2 + (3y2 + 6y + 1) = 0 Reorder the terms: -2 + 5y + -4y2 + (1 + 6y + 3y2) = 0 Remove parenthesis around (1 + 6y + 3y2) -2 + 5y + -4y2 + 1 + 6y + 3y2 = 0 Reorder the terms: -2 + 1 + 5y + 6y + -4y2 + 3y2 = 0 Combine like terms: -2 + 1 = -1 -1 + 5y + 6y + -4y2 + 3y2 = 0 Combine like terms: 5y + 6y = 11y -1 + 11y + -4y2 + 3y2 = 0 Combine like terms: -4y2 + 3y2 = -1y2 -1 + 11y + -1y2 = 0 Solving -1 + 11y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -11y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -11y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -11y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -11y + y2 = 0 + -1 -11y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -11y + y2 = -1 The y term is -11y. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11y + 30.25 + y2 = -1 + 30.25 Reorder the terms: 30.25 + -11y + y2 = -1 + 30.25 Combine like terms: -1 + 30.25 = 29.25 30.25 + -11y + y2 = 29.25 Factor a perfect square on the left side: (y + -5.5)(y + -5.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (y + -5.5) equal to 5.408326913 and -5.408326913.Subproblem 1
y + -5.5 = 5.408326913 Simplifying y + -5.5 = 5.408326913 Reorder the terms: -5.5 + y = 5.408326913 Solving -5.5 + y = 5.408326913 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = 5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = 5.408326913 + 5.5 y = 5.408326913 + 5.5 Combine like terms: 5.408326913 + 5.5 = 10.908326913 y = 10.908326913 Simplifying y = 10.908326913Subproblem 2
y + -5.5 = -5.408326913 Simplifying y + -5.5 = -5.408326913 Reorder the terms: -5.5 + y = -5.408326913 Solving -5.5 + y = -5.408326913 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + y = -5.408326913 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + y = -5.408326913 + 5.5 y = -5.408326913 + 5.5 Combine like terms: -5.408326913 + 5.5 = 0.091673087 y = 0.091673087 Simplifying y = 0.091673087Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.908326913, 0.091673087}
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