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Simplifying m2 + 7m + -129 = 0 Reorder the terms: -129 + 7m + m2 = 0 Solving -129 + 7m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '129' to each side of the equation. -129 + 7m + 129 + m2 = 0 + 129 Reorder the terms: -129 + 129 + 7m + m2 = 0 + 129 Combine like terms: -129 + 129 = 0 0 + 7m + m2 = 0 + 129 7m + m2 = 0 + 129 Combine like terms: 0 + 129 = 129 7m + m2 = 129 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = 129 + 12.25 Reorder the terms: 12.25 + 7m + m2 = 129 + 12.25 Combine like terms: 129 + 12.25 = 141.25 12.25 + 7m + m2 = 141.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 141.25 Calculate the square root of the right side: 11.884864324 Break this problem into two subproblems by setting (m + 3.5) equal to 11.884864324 and -11.884864324.Subproblem 1
m + 3.5 = 11.884864324 Simplifying m + 3.5 = 11.884864324 Reorder the terms: 3.5 + m = 11.884864324 Solving 3.5 + m = 11.884864324 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 11.884864324 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 11.884864324 + -3.5 m = 11.884864324 + -3.5 Combine like terms: 11.884864324 + -3.5 = 8.384864324 m = 8.384864324 Simplifying m = 8.384864324Subproblem 2
m + 3.5 = -11.884864324 Simplifying m + 3.5 = -11.884864324 Reorder the terms: 3.5 + m = -11.884864324 Solving 3.5 + m = -11.884864324 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -11.884864324 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -11.884864324 + -3.5 m = -11.884864324 + -3.5 Combine like terms: -11.884864324 + -3.5 = -15.384864324 m = -15.384864324 Simplifying m = -15.384864324Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.384864324, -15.384864324}
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