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Simplifying 12m + 3m = 12m2 + -96 Combine like terms: 12m + 3m = 15m 15m = 12m2 + -96 Reorder the terms: 15m = -96 + 12m2 Solving 15m = -96 + 12m2 Solving for variable 'm'. Reorder the terms: 96 + 15m + -12m2 = -96 + 12m2 + 96 + -12m2 Reorder the terms: 96 + 15m + -12m2 = -96 + 96 + 12m2 + -12m2 Combine like terms: -96 + 96 = 0 96 + 15m + -12m2 = 0 + 12m2 + -12m2 96 + 15m + -12m2 = 12m2 + -12m2 Combine like terms: 12m2 + -12m2 = 0 96 + 15m + -12m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(32 + 5m + -4m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(32 + 5m + -4m2)' equal to zero and attempt to solve: Simplifying 32 + 5m + -4m2 = 0 Solving 32 + 5m + -4m2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -8 + -1.25m + m2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -1.25m + 8 + m2 = 0 + 8 Reorder the terms: -8 + 8 + -1.25m + m2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1.25m + m2 = 0 + 8 -1.25m + m2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1.25m + m2 = 8 The m term is -1.25m. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25m + 0.390625 + m2 = 8 + 0.390625 Reorder the terms: 0.390625 + -1.25m + m2 = 8 + 0.390625 Combine like terms: 8 + 0.390625 = 8.390625 0.390625 + -1.25m + m2 = 8.390625 Factor a perfect square on the left side: (m + -0.625)(m + -0.625) = 8.390625 Calculate the square root of the right side: 2.896657557 Break this problem into two subproblems by setting (m + -0.625) equal to 2.896657557 and -2.896657557.Subproblem 1
m + -0.625 = 2.896657557 Simplifying m + -0.625 = 2.896657557 Reorder the terms: -0.625 + m = 2.896657557 Solving -0.625 + m = 2.896657557 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + m = 2.896657557 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + m = 2.896657557 + 0.625 m = 2.896657557 + 0.625 Combine like terms: 2.896657557 + 0.625 = 3.521657557 m = 3.521657557 Simplifying m = 3.521657557Subproblem 2
m + -0.625 = -2.896657557 Simplifying m + -0.625 = -2.896657557 Reorder the terms: -0.625 + m = -2.896657557 Solving -0.625 + m = -2.896657557 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + m = -2.896657557 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + m = -2.896657557 + 0.625 m = -2.896657557 + 0.625 Combine like terms: -2.896657557 + 0.625 = -2.271657557 m = -2.271657557 Simplifying m = -2.271657557Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.521657557, -2.271657557}Solution
m = {3.521657557, -2.271657557}
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