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Simplifying 8m2 + -16m + -2 = 0 Reorder the terms: -2 + -16m + 8m2 = 0 Solving -2 + -16m + 8m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -8m + 4m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -8m + 4m2)' equal to zero and attempt to solve: Simplifying -1 + -8m + 4m2 = 0 Solving -1 + -8m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -2m + m2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2m + 0.25 + m2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2m + m2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2m + m2 = 0 + 0.25 -2m + m2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2m + m2 = 0.25 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 0.25 + 1 Reorder the terms: 1 + -2m + m2 = 0.25 + 1 Combine like terms: 0.25 + 1 = 1.25 1 + -2m + m2 = 1.25 Factor a perfect square on the left side: (m + -1)(m + -1) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (m + -1) equal to 1.118033989 and -1.118033989.Subproblem 1
m + -1 = 1.118033989 Simplifying m + -1 = 1.118033989 Reorder the terms: -1 + m = 1.118033989 Solving -1 + m = 1.118033989 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 1.118033989 + 1 Combine like terms: -1 + 1 = 0 0 + m = 1.118033989 + 1 m = 1.118033989 + 1 Combine like terms: 1.118033989 + 1 = 2.118033989 m = 2.118033989 Simplifying m = 2.118033989Subproblem 2
m + -1 = -1.118033989 Simplifying m + -1 = -1.118033989 Reorder the terms: -1 + m = -1.118033989 Solving -1 + m = -1.118033989 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -1.118033989 + 1 Combine like terms: -1 + 1 = 0 0 + m = -1.118033989 + 1 m = -1.118033989 + 1 Combine like terms: -1.118033989 + 1 = -0.118033989 m = -0.118033989 Simplifying m = -0.118033989Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.118033989, -0.118033989}Solution
m = {2.118033989, -0.118033989}
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