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Simplifying 6m + m + -4(2m + 1 + -1m) * m = -8 Reorder the terms: 6m + m + -4(1 + 2m + -1m) * m = -8 Combine like terms: 2m + -1m = 1m 6m + m + -4(1 + 1m) * m = -8 Reorder the terms for easier multiplication: 6m + m + -4m(1 + 1m) = -8 6m + m + (1 * -4m + 1m * -4m) = -8 6m + m + (-4m + -4m2) = -8 Combine like terms: 6m + m = 7m 7m + -4m + -4m2 = -8 Combine like terms: 7m + -4m = 3m 3m + -4m2 = -8 Solving 3m + -4m2 = -8 Solving for variable 'm'. Reorder the terms: 8 + 3m + -4m2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + 3m + -4m2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2 + -0.75m + m2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.75m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + -0.75m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.75m + m2 = 0 + 2 -0.75m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.75m + m2 = 2 The m term is -0.75m. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75m + 0.140625 + m2 = 2 + 0.140625 Reorder the terms: 0.140625 + -0.75m + m2 = 2 + 0.140625 Combine like terms: 2 + 0.140625 = 2.140625 0.140625 + -0.75m + m2 = 2.140625 Factor a perfect square on the left side: (m + -0.375)(m + -0.375) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (m + -0.375) equal to 1.463087489 and -1.463087489.Subproblem 1
m + -0.375 = 1.463087489 Simplifying m + -0.375 = 1.463087489 Reorder the terms: -0.375 + m = 1.463087489 Solving -0.375 + m = 1.463087489 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + m = 1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + m = 1.463087489 + 0.375 m = 1.463087489 + 0.375 Combine like terms: 1.463087489 + 0.375 = 1.838087489 m = 1.838087489 Simplifying m = 1.838087489Subproblem 2
m + -0.375 = -1.463087489 Simplifying m + -0.375 = -1.463087489 Reorder the terms: -0.375 + m = -1.463087489 Solving -0.375 + m = -1.463087489 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + m = -1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + m = -1.463087489 + 0.375 m = -1.463087489 + 0.375 Combine like terms: -1.463087489 + 0.375 = -1.088087489 m = -1.088087489 Simplifying m = -1.088087489Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.838087489, -1.088087489}
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