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Simplifying 2m + 4m(m + -7) = 7m + -4 Reorder the terms: 2m + 4m(-7 + m) = 7m + -4 2m + (-7 * 4m + m * 4m) = 7m + -4 2m + (-28m + 4m2) = 7m + -4 Combine like terms: 2m + -28m = -26m -26m + 4m2 = 7m + -4 Reorder the terms: -26m + 4m2 = -4 + 7m Solving -26m + 4m2 = -4 + 7m Solving for variable 'm'. Reorder the terms: 4 + -26m + -7m + 4m2 = -4 + 7m + 4 + -7m Combine like terms: -26m + -7m = -33m 4 + -33m + 4m2 = -4 + 7m + 4 + -7m Reorder the terms: 4 + -33m + 4m2 = -4 + 4 + 7m + -7m Combine like terms: -4 + 4 = 0 4 + -33m + 4m2 = 0 + 7m + -7m 4 + -33m + 4m2 = 7m + -7m Combine like terms: 7m + -7m = 0 4 + -33m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -8.25m + m2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8.25m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + -8.25m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8.25m + m2 = 0 + -1 -8.25m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8.25m + m2 = -1 The m term is -8.25m. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25m + 17.015625 + m2 = -1 + 17.015625 Reorder the terms: 17.015625 + -8.25m + m2 = -1 + 17.015625 Combine like terms: -1 + 17.015625 = 16.015625 17.015625 + -8.25m + m2 = 16.015625 Factor a perfect square on the left side: (m + -4.125)(m + -4.125) = 16.015625 Calculate the square root of the right side: 4.001952648 Break this problem into two subproblems by setting (m + -4.125) equal to 4.001952648 and -4.001952648.Subproblem 1
m + -4.125 = 4.001952648 Simplifying m + -4.125 = 4.001952648 Reorder the terms: -4.125 + m = 4.001952648 Solving -4.125 + m = 4.001952648 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + m = 4.001952648 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + m = 4.001952648 + 4.125 m = 4.001952648 + 4.125 Combine like terms: 4.001952648 + 4.125 = 8.126952648 m = 8.126952648 Simplifying m = 8.126952648Subproblem 2
m + -4.125 = -4.001952648 Simplifying m + -4.125 = -4.001952648 Reorder the terms: -4.125 + m = -4.001952648 Solving -4.125 + m = -4.001952648 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + m = -4.001952648 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + m = -4.001952648 + 4.125 m = -4.001952648 + 4.125 Combine like terms: -4.001952648 + 4.125 = 0.123047352 m = 0.123047352 Simplifying m = 0.123047352Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.126952648, 0.123047352}
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