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Simplifying y2 + 8y = -6 Reorder the terms: 8y + y2 = -6 Solving 8y + y2 = -6 Solving for variable 'y'. Reorder the terms: 6 + 8y + y2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 8y + -6 + y2 = 0 + -6 Reorder the terms: 6 + -6 + 8y + y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 8y + y2 = 0 + -6 8y + y2 = 0 + -6 Combine like terms: 0 + -6 = -6 8y + y2 = -6 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 = -6 + 16 Reorder the terms: 16 + 8y + y2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + 8y + y2 = 10 Factor a perfect square on the left side: (y + 4)(y + 4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (y + 4) equal to 3.16227766 and -3.16227766.Subproblem 1
y + 4 = 3.16227766 Simplifying y + 4 = 3.16227766 Reorder the terms: 4 + y = 3.16227766 Solving 4 + y = 3.16227766 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 = 3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + y = 3.16227766 + -4 y = 3.16227766 + -4 Combine like terms: 3.16227766 + -4 = -0.83772234 y = -0.83772234 Simplifying y = -0.83772234Subproblem 2
y + 4 = -3.16227766 Simplifying y + 4 = -3.16227766 Reorder the terms: 4 + y = -3.16227766 Solving 4 + y = -3.16227766 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 = -3.16227766 + -4 Combine like terms: 4 + -4 = 0 0 + y = -3.16227766 + -4 y = -3.16227766 + -4 Combine like terms: -3.16227766 + -4 = -7.16227766 y = -7.16227766 Simplifying y = -7.16227766Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.83772234, -7.16227766}
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