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Simplifying 168 + -80m + -8m2 = 0 Solving 168 + -80m + -8m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '8'. 8(21 + -10m + -1m2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(21 + -10m + -1m2)' equal to zero and attempt to solve: Simplifying 21 + -10m + -1m2 = 0 Solving 21 + -10m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 10m + m2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 10m + 21 + m2 = 0 + 21 Reorder the terms: -21 + 21 + 10m + m2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 10m + m2 = 0 + 21 10m + m2 = 0 + 21 Combine like terms: 0 + 21 = 21 10m + m2 = 21 The m term is 10m. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10m + 25 + m2 = 21 + 25 Reorder the terms: 25 + 10m + m2 = 21 + 25 Combine like terms: 21 + 25 = 46 25 + 10m + m2 = 46 Factor a perfect square on the left side: (m + 5)(m + 5) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (m + 5) equal to 6.782329983 and -6.782329983.Subproblem 1
m + 5 = 6.782329983 Simplifying m + 5 = 6.782329983 Reorder the terms: 5 + m = 6.782329983 Solving 5 + m = 6.782329983 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = 6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + m = 6.782329983 + -5 m = 6.782329983 + -5 Combine like terms: 6.782329983 + -5 = 1.782329983 m = 1.782329983 Simplifying m = 1.782329983Subproblem 2
m + 5 = -6.782329983 Simplifying m + 5 = -6.782329983 Reorder the terms: 5 + m = -6.782329983 Solving 5 + m = -6.782329983 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + m = -6.782329983 + -5 Combine like terms: 5 + -5 = 0 0 + m = -6.782329983 + -5 m = -6.782329983 + -5 Combine like terms: -6.782329983 + -5 = -11.782329983 m = -11.782329983 Simplifying m = -11.782329983Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.782329983, -11.782329983}Solution
m = {1.782329983, -11.782329983}
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