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Simplifying y2 + 18y + 53 = 0 Reorder the terms: 53 + 18y + y2 = 0 Solving 53 + 18y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 18y + -53 + y2 = 0 + -53 Reorder the terms: 53 + -53 + 18y + y2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 18y + y2 = 0 + -53 18y + y2 = 0 + -53 Combine like terms: 0 + -53 = -53 18y + y2 = -53 The y term is 18y. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18y + 81 + y2 = -53 + 81 Reorder the terms: 81 + 18y + y2 = -53 + 81 Combine like terms: -53 + 81 = 28 81 + 18y + y2 = 28 Factor a perfect square on the left side: (y + 9)(y + 9) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (y + 9) equal to 5.291502622 and -5.291502622.Subproblem 1
y + 9 = 5.291502622 Simplifying y + 9 = 5.291502622 Reorder the terms: 9 + y = 5.291502622 Solving 9 + y = 5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = 5.291502622 + -9 Combine like terms: 9 + -9 = 0 0 + y = 5.291502622 + -9 y = 5.291502622 + -9 Combine like terms: 5.291502622 + -9 = -3.708497378 y = -3.708497378 Simplifying y = -3.708497378Subproblem 2
y + 9 = -5.291502622 Simplifying y + 9 = -5.291502622 Reorder the terms: 9 + y = -5.291502622 Solving 9 + y = -5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + y = -5.291502622 + -9 Combine like terms: 9 + -9 = 0 0 + y = -5.291502622 + -9 y = -5.291502622 + -9 Combine like terms: -5.291502622 + -9 = -14.291502622 y = -14.291502622 Simplifying y = -14.291502622Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.708497378, -14.291502622}
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