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Simplifying y2 + 12y = y + -5 Reorder the terms: 12y + y2 = y + -5 Reorder the terms: 12y + y2 = -5 + y Solving 12y + y2 = -5 + y Solving for variable 'y'. Reorder the terms: 5 + 12y + -1y + y2 = -5 + y + 5 + -1y Combine like terms: 12y + -1y = 11y 5 + 11y + y2 = -5 + y + 5 + -1y Reorder the terms: 5 + 11y + y2 = -5 + 5 + y + -1y Combine like terms: -5 + 5 = 0 5 + 11y + y2 = 0 + y + -1y 5 + 11y + y2 = y + -1y Combine like terms: y + -1y = 0 5 + 11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 11y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + 11y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 11y + y2 = 0 + -5 11y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 11y + y2 = -5 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 = -5 + 30.25 Reorder the terms: 30.25 + 11y + y2 = -5 + 30.25 Combine like terms: -5 + 30.25 = 25.25 30.25 + 11y + y2 = 25.25 Factor a perfect square on the left side: (y + 5.5)(y + 5.5) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (y + 5.5) equal to 5.024937811 and -5.024937811.Subproblem 1
y + 5.5 = 5.024937811 Simplifying y + 5.5 = 5.024937811 Reorder the terms: 5.5 + y = 5.024937811 Solving 5.5 + y = 5.024937811 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 = 5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 5.024937811 + -5.5 y = 5.024937811 + -5.5 Combine like terms: 5.024937811 + -5.5 = -0.475062189 y = -0.475062189 Simplifying y = -0.475062189Subproblem 2
y + 5.5 = -5.024937811 Simplifying y + 5.5 = -5.024937811 Reorder the terms: 5.5 + y = -5.024937811 Solving 5.5 + y = -5.024937811 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 = -5.024937811 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -5.024937811 + -5.5 y = -5.024937811 + -5.5 Combine like terms: -5.024937811 + -5.5 = -10.524937811 y = -10.524937811 Simplifying y = -10.524937811Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.475062189, -10.524937811}
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