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Simplifying 6m2 + -18m + -16 = 0 Reorder the terms: -16 + -18m + 6m2 = 0 Solving -16 + -18m + 6m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -9m + 3m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -9m + 3m2)' equal to zero and attempt to solve: Simplifying -8 + -9m + 3m2 = 0 Solving -8 + -9m + 3m2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.666666667 + -3m + m2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + -3m + 2.666666667 + m2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + -3m + m2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + -3m + m2 = 0 + 2.666666667 -3m + m2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 -3m + m2 = 2.666666667 The m term is -3m. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3m + 2.25 + m2 = 2.666666667 + 2.25 Reorder the terms: 2.25 + -3m + m2 = 2.666666667 + 2.25 Combine like terms: 2.666666667 + 2.25 = 4.916666667 2.25 + -3m + m2 = 4.916666667 Factor a perfect square on the left side: (m + -1.5)(m + -1.5) = 4.916666667 Calculate the square root of the right side: 2.217355783 Break this problem into two subproblems by setting (m + -1.5) equal to 2.217355783 and -2.217355783.Subproblem 1
m + -1.5 = 2.217355783 Simplifying m + -1.5 = 2.217355783 Reorder the terms: -1.5 + m = 2.217355783 Solving -1.5 + m = 2.217355783 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + m = 2.217355783 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = 2.217355783 + 1.5 m = 2.217355783 + 1.5 Combine like terms: 2.217355783 + 1.5 = 3.717355783 m = 3.717355783 Simplifying m = 3.717355783Subproblem 2
m + -1.5 = -2.217355783 Simplifying m + -1.5 = -2.217355783 Reorder the terms: -1.5 + m = -2.217355783 Solving -1.5 + m = -2.217355783 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + m = -2.217355783 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + m = -2.217355783 + 1.5 m = -2.217355783 + 1.5 Combine like terms: -2.217355783 + 1.5 = -0.717355783 m = -0.717355783 Simplifying m = -0.717355783Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.717355783, -0.717355783}Solution
m = {3.717355783, -0.717355783}
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