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Simplifying m2 + 33m + 130 = 0 Reorder the terms: 130 + 33m + m2 = 0 Solving 130 + 33m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-130' to each side of the equation. 130 + 33m + -130 + m2 = 0 + -130 Reorder the terms: 130 + -130 + 33m + m2 = 0 + -130 Combine like terms: 130 + -130 = 0 0 + 33m + m2 = 0 + -130 33m + m2 = 0 + -130 Combine like terms: 0 + -130 = -130 33m + m2 = -130 The m term is 33m. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33m + 272.25 + m2 = -130 + 272.25 Reorder the terms: 272.25 + 33m + m2 = -130 + 272.25 Combine like terms: -130 + 272.25 = 142.25 272.25 + 33m + m2 = 142.25 Factor a perfect square on the left side: (m + 16.5)(m + 16.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (m + 16.5) equal to 11.926860442 and -11.926860442.Subproblem 1
m + 16.5 = 11.926860442 Simplifying m + 16.5 = 11.926860442 Reorder the terms: 16.5 + m = 11.926860442 Solving 16.5 + m = 11.926860442 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + m = 11.926860442 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + m = 11.926860442 + -16.5 m = 11.926860442 + -16.5 Combine like terms: 11.926860442 + -16.5 = -4.573139558 m = -4.573139558 Simplifying m = -4.573139558Subproblem 2
m + 16.5 = -11.926860442 Simplifying m + 16.5 = -11.926860442 Reorder the terms: 16.5 + m = -11.926860442 Solving 16.5 + m = -11.926860442 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + m = -11.926860442 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + m = -11.926860442 + -16.5 m = -11.926860442 + -16.5 Combine like terms: -11.926860442 + -16.5 = -28.426860442 m = -28.426860442 Simplifying m = -28.426860442Solution
The solution to the problem is based on the solutions from the subproblems. m = {-4.573139558, -28.426860442}
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