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Simplifying 0 = y2 + 2y + -60 Reorder the terms: 0 = -60 + 2y + y2 Solving 0 = -60 + 2y + y2 Solving for variable 'y'. Combine like terms: 0 + 60 = 60 60 + -2y + -1y2 = -60 + 2y + y2 + 60 + -2y + -1y2 Reorder the terms: 60 + -2y + -1y2 = -60 + 60 + 2y + -2y + y2 + -1y2 Combine like terms: -60 + 60 = 0 60 + -2y + -1y2 = 0 + 2y + -2y + y2 + -1y2 60 + -2y + -1y2 = 2y + -2y + y2 + -1y2 Combine like terms: 2y + -2y = 0 60 + -2y + -1y2 = 0 + y2 + -1y2 60 + -2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 60 + -2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + 2y + y2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + 2y + 60 + y2 = 0 + 60 Reorder the terms: -60 + 60 + 2y + y2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 2y + y2 = 0 + 60 2y + y2 = 0 + 60 Combine like terms: 0 + 60 = 60 2y + y2 = 60 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 60 + 1 Reorder the terms: 1 + 2y + y2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + 2y + y2 = 61 Factor a perfect square on the left side: (y + 1)(y + 1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (y + 1) equal to 7.810249676 and -7.810249676.Subproblem 1
y + 1 = 7.810249676 Simplifying y + 1 = 7.810249676 Reorder the terms: 1 + y = 7.810249676 Solving 1 + y = 7.810249676 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + y = 7.810249676 + -1 y = 7.810249676 + -1 Combine like terms: 7.810249676 + -1 = 6.810249676 y = 6.810249676 Simplifying y = 6.810249676Subproblem 2
y + 1 = -7.810249676 Simplifying y + 1 = -7.810249676 Reorder the terms: 1 + y = -7.810249676 Solving 1 + y = -7.810249676 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + y = -7.810249676 + -1 y = -7.810249676 + -1 Combine like terms: -7.810249676 + -1 = -8.810249676 y = -8.810249676 Simplifying y = -8.810249676Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.810249676, -8.810249676}
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