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Simplifying y2 + 13y + -49 = 0 Reorder the terms: -49 + 13y + y2 = 0 Solving -49 + 13y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 13y + 49 + y2 = 0 + 49 Reorder the terms: -49 + 49 + 13y + y2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 13y + y2 = 0 + 49 13y + y2 = 0 + 49 Combine like terms: 0 + 49 = 49 13y + y2 = 49 The y term is 13y. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13y + 42.25 + y2 = 49 + 42.25 Reorder the terms: 42.25 + 13y + y2 = 49 + 42.25 Combine like terms: 49 + 42.25 = 91.25 42.25 + 13y + y2 = 91.25 Factor a perfect square on the left side: (y + 6.5)(y + 6.5) = 91.25 Calculate the square root of the right side: 9.552486587 Break this problem into two subproblems by setting (y + 6.5) equal to 9.552486587 and -9.552486587.Subproblem 1
y + 6.5 = 9.552486587 Simplifying y + 6.5 = 9.552486587 Reorder the terms: 6.5 + y = 9.552486587 Solving 6.5 + y = 9.552486587 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + y = 9.552486587 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = 9.552486587 + -6.5 y = 9.552486587 + -6.5 Combine like terms: 9.552486587 + -6.5 = 3.052486587 y = 3.052486587 Simplifying y = 3.052486587Subproblem 2
y + 6.5 = -9.552486587 Simplifying y + 6.5 = -9.552486587 Reorder the terms: 6.5 + y = -9.552486587 Solving 6.5 + y = -9.552486587 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + y = -9.552486587 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = -9.552486587 + -6.5 y = -9.552486587 + -6.5 Combine like terms: -9.552486587 + -6.5 = -16.052486587 y = -16.052486587 Simplifying y = -16.052486587Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.052486587, -16.052486587}
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