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Simplifying 2m2 + -12m + -2 = 0 Reorder the terms: -2 + -12m + 2m2 = 0 Solving -2 + -12m + 2m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -6m + m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -6m + m2)' equal to zero and attempt to solve: Simplifying -1 + -6m + m2 = 0 Solving -1 + -6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -6m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + -6m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6m + m2 = 0 + 1 -6m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6m + m2 = 1 The m term is -6m. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6m + 9 + m2 = 1 + 9 Reorder the terms: 9 + -6m + m2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6m + m2 = 10 Factor a perfect square on the left side: (m + -3)(m + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (m + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
m + -3 = 3.16227766 Simplifying m + -3 = 3.16227766 Reorder the terms: -3 + m = 3.16227766 Solving -3 + m = 3.16227766 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + m = 3.16227766 + 3 m = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 m = 6.16227766 Simplifying m = 6.16227766Subproblem 2
m + -3 = -3.16227766 Simplifying m + -3 = -3.16227766 Reorder the terms: -3 + m = -3.16227766 Solving -3 + m = -3.16227766 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + m = -3.16227766 + 3 m = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 m = -0.16227766 Simplifying m = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.16227766, -0.16227766}Solution
m = {6.16227766, -0.16227766}
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