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Simplifying 0 = y2 + 3y + -135 Reorder the terms: 0 = -135 + 3y + y2 Solving 0 = -135 + 3y + y2 Solving for variable 'y'. Combine like terms: 0 + 135 = 135 135 + -3y + -1y2 = -135 + 3y + y2 + 135 + -3y + -1y2 Reorder the terms: 135 + -3y + -1y2 = -135 + 135 + 3y + -3y + y2 + -1y2 Combine like terms: -135 + 135 = 0 135 + -3y + -1y2 = 0 + 3y + -3y + y2 + -1y2 135 + -3y + -1y2 = 3y + -3y + y2 + -1y2 Combine like terms: 3y + -3y = 0 135 + -3y + -1y2 = 0 + y2 + -1y2 135 + -3y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 135 + -3y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -135 + 3y + y2 = 0 Move the constant term to the right: Add '135' to each side of the equation. -135 + 3y + 135 + y2 = 0 + 135 Reorder the terms: -135 + 135 + 3y + y2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + 3y + y2 = 0 + 135 3y + y2 = 0 + 135 Combine like terms: 0 + 135 = 135 3y + y2 = 135 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 135 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 135 + 2.25 Combine like terms: 135 + 2.25 = 137.25 2.25 + 3y + y2 = 137.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 137.25 Calculate the square root of the right side: 11.715374514 Break this problem into two subproblems by setting (y + 1.5) equal to 11.715374514 and -11.715374514.Subproblem 1
y + 1.5 = 11.715374514 Simplifying y + 1.5 = 11.715374514 Reorder the terms: 1.5 + y = 11.715374514 Solving 1.5 + y = 11.715374514 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 11.715374514 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 11.715374514 + -1.5 y = 11.715374514 + -1.5 Combine like terms: 11.715374514 + -1.5 = 10.215374514 y = 10.215374514 Simplifying y = 10.215374514Subproblem 2
y + 1.5 = -11.715374514 Simplifying y + 1.5 = -11.715374514 Reorder the terms: 1.5 + y = -11.715374514 Solving 1.5 + y = -11.715374514 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -11.715374514 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -11.715374514 + -1.5 y = -11.715374514 + -1.5 Combine like terms: -11.715374514 + -1.5 = -13.215374514 y = -13.215374514 Simplifying y = -13.215374514Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.215374514, -13.215374514}
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