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Simplifying y2 + 7y + -4 = -4y + 6 Reorder the terms: -4 + 7y + y2 = -4y + 6 Reorder the terms: -4 + 7y + y2 = 6 + -4y Solving -4 + 7y + y2 = 6 + -4y Solving for variable 'y'. Reorder the terms: -4 + -6 + 7y + 4y + y2 = 6 + -4y + -6 + 4y Combine like terms: -4 + -6 = -10 -10 + 7y + 4y + y2 = 6 + -4y + -6 + 4y Combine like terms: 7y + 4y = 11y -10 + 11y + y2 = 6 + -4y + -6 + 4y Reorder the terms: -10 + 11y + y2 = 6 + -6 + -4y + 4y Combine like terms: 6 + -6 = 0 -10 + 11y + y2 = 0 + -4y + 4y -10 + 11y + y2 = -4y + 4y Combine like terms: -4y + 4y = 0 -10 + 11y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 11y + 10 + y2 = 0 + 10 Reorder the terms: -10 + 10 + 11y + y2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 11y + y2 = 0 + 10 11y + y2 = 0 + 10 Combine like terms: 0 + 10 = 10 11y + y2 = 10 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 = 10 + 30.25 Reorder the terms: 30.25 + 11y + y2 = 10 + 30.25 Combine like terms: 10 + 30.25 = 40.25 30.25 + 11y + y2 = 40.25 Factor a perfect square on the left side: (y + 5.5)(y + 5.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (y + 5.5) equal to 6.34428877 and -6.34428877.Subproblem 1
y + 5.5 = 6.34428877 Simplifying y + 5.5 = 6.34428877 Reorder the terms: 5.5 + y = 6.34428877 Solving 5.5 + y = 6.34428877 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 = 6.34428877 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = 6.34428877 + -5.5 y = 6.34428877 + -5.5 Combine like terms: 6.34428877 + -5.5 = 0.84428877 y = 0.84428877 Simplifying y = 0.84428877Subproblem 2
y + 5.5 = -6.34428877 Simplifying y + 5.5 = -6.34428877 Reorder the terms: 5.5 + y = -6.34428877 Solving 5.5 + y = -6.34428877 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 = -6.34428877 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + y = -6.34428877 + -5.5 y = -6.34428877 + -5.5 Combine like terms: -6.34428877 + -5.5 = -11.84428877 y = -11.84428877 Simplifying y = -11.84428877Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.84428877, -11.84428877}
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