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Simplifying y2 + 13y + -100 = 0 Reorder the terms: -100 + 13y + y2 = 0 Solving -100 + 13y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 13y + 100 + y2 = 0 + 100 Reorder the terms: -100 + 100 + 13y + y2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 13y + y2 = 0 + 100 13y + y2 = 0 + 100 Combine like terms: 0 + 100 = 100 13y + y2 = 100 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 = 100 + 42.25 Reorder the terms: 42.25 + 13y + y2 = 100 + 42.25 Combine like terms: 100 + 42.25 = 142.25 42.25 + 13y + y2 = 142.25 Factor a perfect square on the left side: (y + 6.5)(y + 6.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (y + 6.5) equal to 11.926860442 and -11.926860442.Subproblem 1
y + 6.5 = 11.926860442 Simplifying y + 6.5 = 11.926860442 Reorder the terms: 6.5 + y = 11.926860442 Solving 6.5 + y = 11.926860442 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 = 11.926860442 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = 11.926860442 + -6.5 y = 11.926860442 + -6.5 Combine like terms: 11.926860442 + -6.5 = 5.426860442 y = 5.426860442 Simplifying y = 5.426860442Subproblem 2
y + 6.5 = -11.926860442 Simplifying y + 6.5 = -11.926860442 Reorder the terms: 6.5 + y = -11.926860442 Solving 6.5 + y = -11.926860442 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 = -11.926860442 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + y = -11.926860442 + -6.5 y = -11.926860442 + -6.5 Combine like terms: -11.926860442 + -6.5 = -18.426860442 y = -18.426860442 Simplifying y = -18.426860442Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.426860442, -18.426860442}
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