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Simplifying (-4m2 + m + -10) + (3m + 12 + -7m) = 0 Reorder the terms: (-10 + m + -4m2) + (3m + 12 + -7m) = 0 Remove parenthesis around (-10 + m + -4m2) -10 + m + -4m2 + (3m + 12 + -7m) = 0 Reorder the terms: -10 + m + -4m2 + (12 + 3m + -7m) = 0 Combine like terms: 3m + -7m = -4m -10 + m + -4m2 + (12 + -4m) = 0 Remove parenthesis around (12 + -4m) -10 + m + -4m2 + 12 + -4m = 0 Reorder the terms: -10 + 12 + m + -4m + -4m2 = 0 Combine like terms: -10 + 12 = 2 2 + m + -4m + -4m2 = 0 Combine like terms: m + -4m = -3m 2 + -3m + -4m2 = 0 Solving 2 + -3m + -4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.5 + 0.75m + m2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.75m + 0.5 + m2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.75m + m2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.75m + m2 = 0 + 0.5 0.75m + m2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.75m + m2 = 0.5 The m term is 0.75m. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75m + 0.140625 + m2 = 0.5 + 0.140625 Reorder the terms: 0.140625 + 0.75m + m2 = 0.5 + 0.140625 Combine like terms: 0.5 + 0.140625 = 0.640625 0.140625 + 0.75m + m2 = 0.640625 Factor a perfect square on the left side: (m + 0.375)(m + 0.375) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (m + 0.375) equal to 0.80039053 and -0.80039053.Subproblem 1
m + 0.375 = 0.80039053 Simplifying m + 0.375 = 0.80039053 Reorder the terms: 0.375 + m = 0.80039053 Solving 0.375 + m = 0.80039053 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + m = 0.80039053 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + m = 0.80039053 + -0.375 m = 0.80039053 + -0.375 Combine like terms: 0.80039053 + -0.375 = 0.42539053 m = 0.42539053 Simplifying m = 0.42539053Subproblem 2
m + 0.375 = -0.80039053 Simplifying m + 0.375 = -0.80039053 Reorder the terms: 0.375 + m = -0.80039053 Solving 0.375 + m = -0.80039053 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + m = -0.80039053 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + m = -0.80039053 + -0.375 m = -0.80039053 + -0.375 Combine like terms: -0.80039053 + -0.375 = -1.17539053 m = -1.17539053 Simplifying m = -1.17539053Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.42539053, -1.17539053}
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