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Simplifying (8m2 + 4m + -7) + -1(2m2 + -5m + 2) = 0 Reorder the terms: (-7 + 4m + 8m2) + -1(2m2 + -5m + 2) = 0 Remove parenthesis around (-7 + 4m + 8m2) -7 + 4m + 8m2 + -1(2m2 + -5m + 2) = 0 Reorder the terms: -7 + 4m + 8m2 + -1(2 + -5m + 2m2) = 0 -7 + 4m + 8m2 + (2 * -1 + -5m * -1 + 2m2 * -1) = 0 -7 + 4m + 8m2 + (-2 + 5m + -2m2) = 0 Reorder the terms: -7 + -2 + 4m + 5m + 8m2 + -2m2 = 0 Combine like terms: -7 + -2 = -9 -9 + 4m + 5m + 8m2 + -2m2 = 0 Combine like terms: 4m + 5m = 9m -9 + 9m + 8m2 + -2m2 = 0 Combine like terms: 8m2 + -2m2 = 6m2 -9 + 9m + 6m2 = 0 Solving -9 + 9m + 6m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 3m + 2m2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + 3m + 2m2)' equal to zero and attempt to solve: Simplifying -3 + 3m + 2m2 = 0 Solving -3 + 3m + 2m2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 1.5m + m2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 1.5m + 1.5 + m2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 1.5m + m2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 1.5m + m2 = 0 + 1.5 1.5m + m2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 1.5m + m2 = 1.5 The m term is 1.5m. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5m + 0.5625 + m2 = 1.5 + 0.5625 Reorder the terms: 0.5625 + 1.5m + m2 = 1.5 + 0.5625 Combine like terms: 1.5 + 0.5625 = 2.0625 0.5625 + 1.5m + m2 = 2.0625 Factor a perfect square on the left side: (m + 0.75)(m + 0.75) = 2.0625 Calculate the square root of the right side: 1.436140662 Break this problem into two subproblems by setting (m + 0.75) equal to 1.436140662 and -1.436140662.Subproblem 1
m + 0.75 = 1.436140662 Simplifying m + 0.75 = 1.436140662 Reorder the terms: 0.75 + m = 1.436140662 Solving 0.75 + m = 1.436140662 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m = 1.436140662 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m = 1.436140662 + -0.75 m = 1.436140662 + -0.75 Combine like terms: 1.436140662 + -0.75 = 0.686140662 m = 0.686140662 Simplifying m = 0.686140662Subproblem 2
m + 0.75 = -1.436140662 Simplifying m + 0.75 = -1.436140662 Reorder the terms: 0.75 + m = -1.436140662 Solving 0.75 + m = -1.436140662 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + m = -1.436140662 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m = -1.436140662 + -0.75 m = -1.436140662 + -0.75 Combine like terms: -1.436140662 + -0.75 = -2.186140662 m = -2.186140662 Simplifying m = -2.186140662Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.686140662, -2.186140662}Solution
m = {0.686140662, -2.186140662}
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