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Simplifying 10m2 + -8m + -16 = -10m + 2m2 Reorder the terms: -16 + -8m + 10m2 = -10m + 2m2 Solving -16 + -8m + 10m2 = -10m + 2m2 Solving for variable 'm'. Reorder the terms: -16 + -8m + 10m + 10m2 + -2m2 = -10m + 2m2 + 10m + -2m2 Combine like terms: -8m + 10m = 2m -16 + 2m + 10m2 + -2m2 = -10m + 2m2 + 10m + -2m2 Combine like terms: 10m2 + -2m2 = 8m2 -16 + 2m + 8m2 = -10m + 2m2 + 10m + -2m2 Reorder the terms: -16 + 2m + 8m2 = -10m + 10m + 2m2 + -2m2 Combine like terms: -10m + 10m = 0 -16 + 2m + 8m2 = 0 + 2m2 + -2m2 -16 + 2m + 8m2 = 2m2 + -2m2 Combine like terms: 2m2 + -2m2 = 0 -16 + 2m + 8m2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + m + 4m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + m + 4m2)' equal to zero and attempt to solve: Simplifying -8 + m + 4m2 = 0 Solving -8 + m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 0.25m + m2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.25m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + 0.25m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.25m + m2 = 0 + 2 0.25m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.25m + m2 = 2 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. 0.25m + 0.25 + m2 = 2 + 0.25 Reorder the terms: 0.25 + 0.25m + m2 = 2 + 0.25 Combine like terms: 2 + 0.25 = 2.25 0.25 + 0.25m + m2 = 2.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (m + 0.5) equal to 1.5 and -1.5.Subproblem 1
m + 0.5 = 1.5 Simplifying m + 0.5 = 1.5 Reorder the terms: 0.5 + m = 1.5 Solving 0.5 + m = 1.5 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 = 1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.5 + -0.5 m = 1.5 + -0.5 Combine like terms: 1.5 + -0.5 = 1 m = 1 Simplifying m = 1Subproblem 2
m + 0.5 = -1.5 Simplifying m + 0.5 = -1.5 Reorder the terms: 0.5 + m = -1.5 Solving 0.5 + m = -1.5 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 = -1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.5 + -0.5 m = -1.5 + -0.5 Combine like terms: -1.5 + -0.5 = -2 m = -2 Simplifying m = -2Solution
The solution to the problem is based on the solutions from the subproblems. m = {1, -2}Solution
m = {1, -2}
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