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Simplifying 2m2 = 32 + -8m Solving 2m2 = 32 + -8m Solving for variable 'm'. Reorder the terms: -32 + 8m + 2m2 = 32 + -8m + -32 + 8m Reorder the terms: -32 + 8m + 2m2 = 32 + -32 + -8m + 8m Combine like terms: 32 + -32 = 0 -32 + 8m + 2m2 = 0 + -8m + 8m -32 + 8m + 2m2 = -8m + 8m Combine like terms: -8m + 8m = 0 -32 + 8m + 2m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + 4m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + 4m + m2)' equal to zero and attempt to solve: Simplifying -16 + 4m + m2 = 0 Solving -16 + 4m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 4m + 16 + m2 = 0 + 16 Reorder the terms: -16 + 16 + 4m + m2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 4m + m2 = 0 + 16 4m + m2 = 0 + 16 Combine like terms: 0 + 16 = 16 4m + m2 = 16 The m term is 4m. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4m + 4 + m2 = 16 + 4 Reorder the terms: 4 + 4m + m2 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + 4m + m2 = 20 Factor a perfect square on the left side: (m + 2)(m + 2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (m + 2) equal to 4.472135955 and -4.472135955.Subproblem 1
m + 2 = 4.472135955 Simplifying m + 2 = 4.472135955 Reorder the terms: 2 + m = 4.472135955 Solving 2 + m = 4.472135955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = 4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + m = 4.472135955 + -2 m = 4.472135955 + -2 Combine like terms: 4.472135955 + -2 = 2.472135955 m = 2.472135955 Simplifying m = 2.472135955Subproblem 2
m + 2 = -4.472135955 Simplifying m + 2 = -4.472135955 Reorder the terms: 2 + m = -4.472135955 Solving 2 + m = -4.472135955 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + m = -4.472135955 + -2 Combine like terms: 2 + -2 = 0 0 + m = -4.472135955 + -2 m = -4.472135955 + -2 Combine like terms: -4.472135955 + -2 = -6.472135955 m = -6.472135955 Simplifying m = -6.472135955Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.472135955, -6.472135955}Solution
m = {2.472135955, -6.472135955}
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