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Simplifying (4m2 + -3m + 1) + (m2 + m + -2) = 0 Reorder the terms: (1 + -3m + 4m2) + (m2 + m + -2) = 0 Remove parenthesis around (1 + -3m + 4m2) 1 + -3m + 4m2 + (m2 + m + -2) = 0 Reorder the terms: 1 + -3m + 4m2 + (-2 + m + m2) = 0 Remove parenthesis around (-2 + m + m2) 1 + -3m + 4m2 + -2 + m + m2 = 0 Reorder the terms: 1 + -2 + -3m + m + 4m2 + m2 = 0 Combine like terms: 1 + -2 = -1 -1 + -3m + m + 4m2 + m2 = 0 Combine like terms: -3m + m = -2m -1 + -2m + 4m2 + m2 = 0 Combine like terms: 4m2 + m2 = 5m2 -1 + -2m + 5m2 = 0 Solving -1 + -2m + 5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -0.4m + m2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.4m + 0.2 + m2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.4m + m2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.4m + m2 = 0 + 0.2 -0.4m + m2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -0.4m + m2 = 0.2 The m term is -0.4m. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4m + 0.04 + m2 = 0.2 + 0.04 Reorder the terms: 0.04 + -0.4m + m2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + -0.4m + m2 = 0.24 Factor a perfect square on the left side: (m + -0.2)(m + -0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (m + -0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
m + -0.2 = 0.489897949 Simplifying m + -0.2 = 0.489897949 Reorder the terms: -0.2 + m = 0.489897949 Solving -0.2 + m = 0.489897949 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = 0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = 0.489897949 + 0.2 m = 0.489897949 + 0.2 Combine like terms: 0.489897949 + 0.2 = 0.689897949 m = 0.689897949 Simplifying m = 0.689897949Subproblem 2
m + -0.2 = -0.489897949 Simplifying m + -0.2 = -0.489897949 Reorder the terms: -0.2 + m = -0.489897949 Solving -0.2 + m = -0.489897949 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + m = -0.489897949 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + m = -0.489897949 + 0.2 m = -0.489897949 + 0.2 Combine like terms: -0.489897949 + 0.2 = -0.289897949 m = -0.289897949 Simplifying m = -0.289897949Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.689897949, -0.289897949}
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