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Simplifying 4m2 + -2m = 8 Reorder the terms: -2m + 4m2 = 8 Solving -2m + 4m2 = 8 Solving for variable 'm'. Reorder the terms: -8 + -2m + 4m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -2m + 4m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -1m + 2m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -1m + 2m2)' equal to zero and attempt to solve: Simplifying -4 + -1m + 2m2 = 0 Solving -4 + -1m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + -0.5m + m2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.5m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + -0.5m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.5m + m2 = 0 + 2 -0.5m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.5m + m2 = 2 The m term is -0.5m. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5m + 0.0625 + m2 = 2 + 0.0625 Reorder the terms: 0.0625 + -0.5m + m2 = 2 + 0.0625 Combine like terms: 2 + 0.0625 = 2.0625 0.0625 + -0.5m + m2 = 2.0625 Factor a perfect square on the left side: (m + -0.25)(m + -0.25) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (m + -0.25) equal to 1.436140662 and -1.436140662.Subproblem 1
m + -0.25 = 1.436140662 Simplifying m + -0.25 = 1.436140662 Reorder the terms: -0.25 + m = 1.436140662 Solving -0.25 + m = 1.436140662 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + m = 1.436140662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = 1.436140662 + 0.25 m = 1.436140662 + 0.25 Combine like terms: 1.436140662 + 0.25 = 1.686140662 m = 1.686140662 Simplifying m = 1.686140662Subproblem 2
m + -0.25 = -1.436140662 Simplifying m + -0.25 = -1.436140662 Reorder the terms: -0.25 + m = -1.436140662 Solving -0.25 + m = -1.436140662 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + m = -1.436140662 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = -1.436140662 + 0.25 m = -1.436140662 + 0.25 Combine like terms: -1.436140662 + 0.25 = -1.186140662 m = -1.186140662 Simplifying m = -1.186140662Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.686140662, -1.186140662}Solution
m = {1.686140662, -1.186140662}
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