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Simplifying 111 = -3(1 + -8m) * 5m Reorder the terms for easier multiplication: 111 = -3 * 5m(1 + -8m) Multiply -3 * 5 111 = -15m(1 + -8m) 111 = (1 * -15m + -8m * -15m) 111 = (-15m + 120m2) Solving 111 = -15m + 120m2 Solving for variable 'm'. Reorder the terms: 111 + 15m + -120m2 = -15m + 15m + 120m2 + -120m2 Combine like terms: -15m + 15m = 0 111 + 15m + -120m2 = 0 + 120m2 + -120m2 111 + 15m + -120m2 = 120m2 + -120m2 Combine like terms: 120m2 + -120m2 = 0 111 + 15m + -120m2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(37 + 5m + -40m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(37 + 5m + -40m2)' equal to zero and attempt to solve: Simplifying 37 + 5m + -40m2 = 0 Solving 37 + 5m + -40m2 = 0 Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.925 + -0.125m + m2 = 0.0 Move the constant term to the right: Add '0.925' to each side of the equation. -0.925 + -0.125m + 0.925 + m2 = 0.0 + 0.925 Reorder the terms: -0.925 + 0.925 + -0.125m + m2 = 0.0 + 0.925 Combine like terms: -0.925 + 0.925 = 0.000 0.000 + -0.125m + m2 = 0.0 + 0.925 -0.125m + m2 = 0.0 + 0.925 Combine like terms: 0.0 + 0.925 = 0.925 -0.125m + m2 = 0.925 The m term is -0.125m. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125m + 0.00390625 + m2 = 0.925 + 0.00390625 Reorder the terms: 0.00390625 + -0.125m + m2 = 0.925 + 0.00390625 Combine like terms: 0.925 + 0.00390625 = 0.92890625 0.00390625 + -0.125m + m2 = 0.92890625 Factor a perfect square on the left side: (m + -0.0625)(m + -0.0625) = 0.92890625 Calculate the square root of the right side: 0.963797826 Break this problem into two subproblems by setting (m + -0.0625) equal to 0.963797826 and -0.963797826.Subproblem 1
m + -0.0625 = 0.963797826 Simplifying m + -0.0625 = 0.963797826 Reorder the terms: -0.0625 + m = 0.963797826 Solving -0.0625 + m = 0.963797826 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + m = 0.963797826 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + m = 0.963797826 + 0.0625 m = 0.963797826 + 0.0625 Combine like terms: 0.963797826 + 0.0625 = 1.026297826 m = 1.026297826 Simplifying m = 1.026297826Subproblem 2
m + -0.0625 = -0.963797826 Simplifying m + -0.0625 = -0.963797826 Reorder the terms: -0.0625 + m = -0.963797826 Solving -0.0625 + m = -0.963797826 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + m = -0.963797826 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + m = -0.963797826 + 0.0625 m = -0.963797826 + 0.0625 Combine like terms: -0.963797826 + 0.0625 = -0.901297826 m = -0.901297826 Simplifying m = -0.901297826Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.026297826, -0.901297826}Solution
m = {1.026297826, -0.901297826}
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