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Simplifying (6y2 + -3y + -5) + -1(4y2 + 5) + -1(8y + 5) = 0 Reorder the terms: (-5 + -3y + 6y2) + -1(4y2 + 5) + -1(8y + 5) = 0 Remove parenthesis around (-5 + -3y + 6y2) -5 + -3y + 6y2 + -1(4y2 + 5) + -1(8y + 5) = 0 Reorder the terms: -5 + -3y + 6y2 + -1(5 + 4y2) + -1(8y + 5) = 0 -5 + -3y + 6y2 + (5 * -1 + 4y2 * -1) + -1(8y + 5) = 0 -5 + -3y + 6y2 + (-5 + -4y2) + -1(8y + 5) = 0 Reorder the terms: -5 + -3y + 6y2 + -5 + -4y2 + -1(5 + 8y) = 0 -5 + -3y + 6y2 + -5 + -4y2 + (5 * -1 + 8y * -1) = 0 -5 + -3y + 6y2 + -5 + -4y2 + (-5 + -8y) = 0 Reorder the terms: -5 + -5 + -5 + -3y + -8y + 6y2 + -4y2 = 0 Combine like terms: -5 + -5 = -10 -10 + -5 + -3y + -8y + 6y2 + -4y2 = 0 Combine like terms: -10 + -5 = -15 -15 + -3y + -8y + 6y2 + -4y2 = 0 Combine like terms: -3y + -8y = -11y -15 + -11y + 6y2 + -4y2 = 0 Combine like terms: 6y2 + -4y2 = 2y2 -15 + -11y + 2y2 = 0 Solving -15 + -11y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -5.5y + y2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -5.5y + 7.5 + y2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -5.5y + y2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -5.5y + y2 = 0 + 7.5 -5.5y + y2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -5.5y + y2 = 7.5 The y term is -5.5y. Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. -5.5y + 7.5625 + y2 = 7.5 + 7.5625 Reorder the terms: 7.5625 + -5.5y + y2 = 7.5 + 7.5625 Combine like terms: 7.5 + 7.5625 = 15.0625 7.5625 + -5.5y + y2 = 15.0625 Factor a perfect square on the left side: (y + -2.75)(y + -2.75) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (y + -2.75) equal to 3.881043674 and -3.881043674.Subproblem 1
y + -2.75 = 3.881043674 Simplifying y + -2.75 = 3.881043674 Reorder the terms: -2.75 + y = 3.881043674 Solving -2.75 + y = 3.881043674 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = 3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = 3.881043674 + 2.75 y = 3.881043674 + 2.75 Combine like terms: 3.881043674 + 2.75 = 6.631043674 y = 6.631043674 Simplifying y = 6.631043674Subproblem 2
y + -2.75 = -3.881043674 Simplifying y + -2.75 = -3.881043674 Reorder the terms: -2.75 + y = -3.881043674 Solving -2.75 + y = -3.881043674 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + y = -3.881043674 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + y = -3.881043674 + 2.75 y = -3.881043674 + 2.75 Combine like terms: -3.881043674 + 2.75 = -1.131043674 y = -1.131043674 Simplifying y = -1.131043674Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.631043674, -1.131043674}
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