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Simplifying -9 = 3(m + -5) * m Reorder the terms: -9 = 3(-5 + m) * m Reorder the terms for easier multiplication: -9 = 3m(-5 + m) -9 = (-5 * 3m + m * 3m) -9 = (-15m + 3m2) Solving -9 = -15m + 3m2 Solving for variable 'm'. Reorder the terms: -9 + 15m + -3m2 = -15m + 15m + 3m2 + -3m2 Combine like terms: -15m + 15m = 0 -9 + 15m + -3m2 = 0 + 3m2 + -3m2 -9 + 15m + -3m2 = 3m2 + -3m2 Combine like terms: 3m2 + -3m2 = 0 -9 + 15m + -3m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 5m + -1m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 5m + -1m2)' equal to zero and attempt to solve: Simplifying -3 + 5m + -1m2 = 0 Solving -3 + 5m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -5m + m2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5m + -3 + m2 = 0 + -3 Reorder the terms: 3 + -3 + -5m + m2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5m + m2 = 0 + -3 -5m + m2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5m + m2 = -3 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = -3 + 6.25 Reorder the terms: 6.25 + -5m + m2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + -5m + m2 = 3.25 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (m + -2.5) equal to 1.802775638 and -1.802775638.Subproblem 1
m + -2.5 = 1.802775638 Simplifying m + -2.5 = 1.802775638 Reorder the terms: -2.5 + m = 1.802775638 Solving -2.5 + m = 1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 1.802775638 + 2.5 m = 1.802775638 + 2.5 Combine like terms: 1.802775638 + 2.5 = 4.302775638 m = 4.302775638 Simplifying m = 4.302775638Subproblem 2
m + -2.5 = -1.802775638 Simplifying m + -2.5 = -1.802775638 Reorder the terms: -2.5 + m = -1.802775638 Solving -2.5 + m = -1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -1.802775638 + 2.5 m = -1.802775638 + 2.5 Combine like terms: -1.802775638 + 2.5 = 0.697224362 m = 0.697224362 Simplifying m = 0.697224362Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.302775638, 0.697224362}Solution
m = {4.302775638, 0.697224362}
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