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Simplifying y2 + -35y + 15 = 0 Reorder the terms: 15 + -35y + y2 = 0 Solving 15 + -35y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -35y + -15 + y2 = 0 + -15 Reorder the terms: 15 + -15 + -35y + y2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -35y + y2 = 0 + -15 -35y + y2 = 0 + -15 Combine like terms: 0 + -15 = -15 -35y + y2 = -15 The y term is -35y. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35y + 306.25 + y2 = -15 + 306.25 Reorder the terms: 306.25 + -35y + y2 = -15 + 306.25 Combine like terms: -15 + 306.25 = 291.25 306.25 + -35y + y2 = 291.25 Factor a perfect square on the left side: (y + -17.5)(y + -17.5) = 291.25 Calculate the square root of the right side: 17.066048166 Break this problem into two subproblems by setting (y + -17.5) equal to 17.066048166 and -17.066048166.Subproblem 1
y + -17.5 = 17.066048166 Simplifying y + -17.5 = 17.066048166 Reorder the terms: -17.5 + y = 17.066048166 Solving -17.5 + y = 17.066048166 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + y = 17.066048166 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + y = 17.066048166 + 17.5 y = 17.066048166 + 17.5 Combine like terms: 17.066048166 + 17.5 = 34.566048166 y = 34.566048166 Simplifying y = 34.566048166Subproblem 2
y + -17.5 = -17.066048166 Simplifying y + -17.5 = -17.066048166 Reorder the terms: -17.5 + y = -17.066048166 Solving -17.5 + y = -17.066048166 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + y = -17.066048166 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + y = -17.066048166 + 17.5 y = -17.066048166 + 17.5 Combine like terms: -17.066048166 + 17.5 = 0.433951834 y = 0.433951834 Simplifying y = 0.433951834Solution
The solution to the problem is based on the solutions from the subproblems. y = {34.566048166, 0.433951834}
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