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Simplifying m(30m + -175) = 25 Reorder the terms: m(-175 + 30m) = 25 (-175 * m + 30m * m) = 25 (-175m + 30m2) = 25 Solving -175m + 30m2 = 25 Solving for variable 'm'. Reorder the terms: -25 + -175m + 30m2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -175m + 30m2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + -35m + 6m2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -35m + 6m2)' equal to zero and attempt to solve: Simplifying -5 + -35m + 6m2 = 0 Solving -5 + -35m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -5.833333333m + m2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -5.833333333m + 0.8333333333 + m2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -5.833333333m + m2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -5.833333333m + m2 = 0 + 0.8333333333 -5.833333333m + m2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -5.833333333m + m2 = 0.8333333333 The m term is -5.833333333m. Take half its coefficient (-2.916666667). Square it (8.506944446) and add it to both sides. Add '8.506944446' to each side of the equation. -5.833333333m + 8.506944446 + m2 = 0.8333333333 + 8.506944446 Reorder the terms: 8.506944446 + -5.833333333m + m2 = 0.8333333333 + 8.506944446 Combine like terms: 0.8333333333 + 8.506944446 = 9.3402777793 8.506944446 + -5.833333333m + m2 = 9.3402777793 Factor a perfect square on the left side: (m + -2.916666667)(m + -2.916666667) = 9.3402777793 Calculate the square root of the right side: 3.056186804 Break this problem into two subproblems by setting (m + -2.916666667) equal to 3.056186804 and -3.056186804.Subproblem 1
m + -2.916666667 = 3.056186804 Simplifying m + -2.916666667 = 3.056186804 Reorder the terms: -2.916666667 + m = 3.056186804 Solving -2.916666667 + m = 3.056186804 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + m = 3.056186804 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + m = 3.056186804 + 2.916666667 m = 3.056186804 + 2.916666667 Combine like terms: 3.056186804 + 2.916666667 = 5.972853471 m = 5.972853471 Simplifying m = 5.972853471Subproblem 2
m + -2.916666667 = -3.056186804 Simplifying m + -2.916666667 = -3.056186804 Reorder the terms: -2.916666667 + m = -3.056186804 Solving -2.916666667 + m = -3.056186804 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.916666667' to each side of the equation. -2.916666667 + 2.916666667 + m = -3.056186804 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + m = -3.056186804 + 2.916666667 m = -3.056186804 + 2.916666667 Combine like terms: -3.056186804 + 2.916666667 = -0.139520137 m = -0.139520137 Simplifying m = -0.139520137Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.972853471, -0.139520137}Solution
m = {5.972853471, -0.139520137}
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