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Simplifying y2 + -3y = 49 Reorder the terms: -3y + y2 = 49 Solving -3y + y2 = 49 Solving for variable 'y'. Reorder the terms: -49 + -3y + y2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -3y + 49 + y2 = 0 + 49 Reorder the terms: -49 + 49 + -3y + y2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -3y + y2 = 0 + 49 -3y + y2 = 0 + 49 Combine like terms: 0 + 49 = 49 -3y + y2 = 49 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 49 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 49 + 2.25 Combine like terms: 49 + 2.25 = 51.25 2.25 + -3y + y2 = 51.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (y + -1.5) equal to 7.158910532 and -7.158910532.Subproblem 1
y + -1.5 = 7.158910532 Simplifying y + -1.5 = 7.158910532 Reorder the terms: -1.5 + y = 7.158910532 Solving -1.5 + y = 7.158910532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 7.158910532 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 7.158910532 + 1.5 y = 7.158910532 + 1.5 Combine like terms: 7.158910532 + 1.5 = 8.658910532 y = 8.658910532 Simplifying y = 8.658910532Subproblem 2
y + -1.5 = -7.158910532 Simplifying y + -1.5 = -7.158910532 Reorder the terms: -1.5 + y = -7.158910532 Solving -1.5 + y = -7.158910532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -7.158910532 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -7.158910532 + 1.5 y = -7.158910532 + 1.5 Combine like terms: -7.158910532 + 1.5 = -5.658910532 y = -5.658910532 Simplifying y = -5.658910532Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.658910532, -5.658910532}
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