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Simplifying y2 + -8y + -152 = 0 Reorder the terms: -152 + -8y + y2 = 0 Solving -152 + -8y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '152' to each side of the equation. -152 + -8y + 152 + y2 = 0 + 152 Reorder the terms: -152 + 152 + -8y + y2 = 0 + 152 Combine like terms: -152 + 152 = 0 0 + -8y + y2 = 0 + 152 -8y + y2 = 0 + 152 Combine like terms: 0 + 152 = 152 -8y + y2 = 152 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 152 + 16 Reorder the terms: 16 + -8y + y2 = 152 + 16 Combine like terms: 152 + 16 = 168 16 + -8y + y2 = 168 Factor a perfect square on the left side: (y + -4)(y + -4) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (y + -4) equal to 12.961481397 and -12.961481397.Subproblem 1
y + -4 = 12.961481397 Simplifying y + -4 = 12.961481397 Reorder the terms: -4 + y = 12.961481397 Solving -4 + y = 12.961481397 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 12.961481397 + 4 Combine like terms: -4 + 4 = 0 0 + y = 12.961481397 + 4 y = 12.961481397 + 4 Combine like terms: 12.961481397 + 4 = 16.961481397 y = 16.961481397 Simplifying y = 16.961481397Subproblem 2
y + -4 = -12.961481397 Simplifying y + -4 = -12.961481397 Reorder the terms: -4 + y = -12.961481397 Solving -4 + y = -12.961481397 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -12.961481397 + 4 Combine like terms: -4 + 4 = 0 0 + y = -12.961481397 + 4 y = -12.961481397 + 4 Combine like terms: -12.961481397 + 4 = -8.961481397 y = -8.961481397 Simplifying y = -8.961481397Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.961481397, -8.961481397}
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