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Simplifying 9m2 = -3m + 15 Reorder the terms: 9m2 = 15 + -3m Solving 9m2 = 15 + -3m Solving for variable 'm'. Reorder the terms: -15 + 3m + 9m2 = 15 + -3m + -15 + 3m Reorder the terms: -15 + 3m + 9m2 = 15 + -15 + -3m + 3m Combine like terms: 15 + -15 = 0 -15 + 3m + 9m2 = 0 + -3m + 3m -15 + 3m + 9m2 = -3m + 3m Combine like terms: -3m + 3m = 0 -15 + 3m + 9m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + m + 3m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + m + 3m2)' equal to zero and attempt to solve: Simplifying -5 + m + 3m2 = 0 Solving -5 + m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + 0.3333333333m + m2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 0.3333333333m + 1.666666667 + m2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 0.3333333333m + m2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 0.3333333333m + m2 = 0 + 1.666666667 0.3333333333m + m2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 0.3333333333m + m2 = 1.666666667 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333m + 0.25 + m2 = 1.666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333m + m2 = 1.666666667 + 0.25 Combine like terms: 1.666666667 + 0.25 = 1.916666667 0.25 + 0.3333333333m + m2 = 1.916666667 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 1.916666667 Calculate the square root of the right side: 1.384437311 Break this problem into two subproblems by setting (m + 0.5) equal to 1.384437311 and -1.384437311.Subproblem 1
m + 0.5 = 1.384437311 Simplifying m + 0.5 = 1.384437311 Reorder the terms: 0.5 + m = 1.384437311 Solving 0.5 + m = 1.384437311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 1.384437311 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.384437311 + -0.5 m = 1.384437311 + -0.5 Combine like terms: 1.384437311 + -0.5 = 0.884437311 m = 0.884437311 Simplifying m = 0.884437311Subproblem 2
m + 0.5 = -1.384437311 Simplifying m + 0.5 = -1.384437311 Reorder the terms: 0.5 + m = -1.384437311 Solving 0.5 + m = -1.384437311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -1.384437311 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.384437311 + -0.5 m = -1.384437311 + -0.5 Combine like terms: -1.384437311 + -0.5 = -1.884437311 m = -1.884437311 Simplifying m = -1.884437311Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.884437311, -1.884437311}Solution
m = {0.884437311, -1.884437311}
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