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Simplifying y2 + 6y + 8.75 = 0 Reorder the terms: 8.75 + 6y + y2 = 0 Solving 8.75 + 6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + 6y + -8.75 + y2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + 6y + y2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + 6y + y2 = 0 + -8.75 6y + y2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 6y + y2 = -8.75 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -8.75 + 9 Reorder the terms: 9 + 6y + y2 = -8.75 + 9 Combine like terms: -8.75 + 9 = 0.25 9 + 6y + y2 = 0.25 Factor a perfect square on the left side: (y + 3)(y + 3) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (y + 3) equal to 0.5 and -0.5.Subproblem 1
y + 3 = 0.5 Simplifying y + 3 = 0.5 Reorder the terms: 3 + y = 0.5 Solving 3 + y = 0.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 0.5 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0.5 + -3 y = 0.5 + -3 Combine like terms: 0.5 + -3 = -2.5 y = -2.5 Simplifying y = -2.5Subproblem 2
y + 3 = -0.5 Simplifying y + 3 = -0.5 Reorder the terms: 3 + y = -0.5 Solving 3 + y = -0.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -0.5 + -3 Combine like terms: 3 + -3 = 0 0 + y = -0.5 + -3 y = -0.5 + -3 Combine like terms: -0.5 + -3 = -3.5 y = -3.5 Simplifying y = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.5, -3.5}
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