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Simplifying -2m2 + 2m = 8m + m2 + -4 Reorder the terms: 2m + -2m2 = 8m + m2 + -4 Reorder the terms: 2m + -2m2 = -4 + 8m + m2 Solving 2m + -2m2 = -4 + 8m + m2 Solving for variable 'm'. Reorder the terms: 4 + 2m + -8m + -2m2 + -1m2 = -4 + 8m + m2 + 4 + -8m + -1m2 Combine like terms: 2m + -8m = -6m 4 + -6m + -2m2 + -1m2 = -4 + 8m + m2 + 4 + -8m + -1m2 Combine like terms: -2m2 + -1m2 = -3m2 4 + -6m + -3m2 = -4 + 8m + m2 + 4 + -8m + -1m2 Reorder the terms: 4 + -6m + -3m2 = -4 + 4 + 8m + -8m + m2 + -1m2 Combine like terms: -4 + 4 = 0 4 + -6m + -3m2 = 0 + 8m + -8m + m2 + -1m2 4 + -6m + -3m2 = 8m + -8m + m2 + -1m2 Combine like terms: 8m + -8m = 0 4 + -6m + -3m2 = 0 + m2 + -1m2 4 + -6m + -3m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 4 + -6m + -3m2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + 2m + m2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 2m + 1.333333333 + m2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 2m + m2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 2m + m2 = 0 + 1.333333333 2m + m2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 2m + m2 = 1.333333333 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 = 1.333333333 + 1 Reorder the terms: 1 + 2m + m2 = 1.333333333 + 1 Combine like terms: 1.333333333 + 1 = 2.333333333 1 + 2m + m2 = 2.333333333 Factor a perfect square on the left side: (m + 1)(m + 1) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (m + 1) equal to 1.527525232 and -1.527525232.Subproblem 1
m + 1 = 1.527525232 Simplifying m + 1 = 1.527525232 Reorder the terms: 1 + m = 1.527525232 Solving 1 + m = 1.527525232 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 = 1.527525232 + -1 Combine like terms: 1 + -1 = 0 0 + m = 1.527525232 + -1 m = 1.527525232 + -1 Combine like terms: 1.527525232 + -1 = 0.527525232 m = 0.527525232 Simplifying m = 0.527525232Subproblem 2
m + 1 = -1.527525232 Simplifying m + 1 = -1.527525232 Reorder the terms: 1 + m = -1.527525232 Solving 1 + m = -1.527525232 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 = -1.527525232 + -1 Combine like terms: 1 + -1 = 0 0 + m = -1.527525232 + -1 m = -1.527525232 + -1 Combine like terms: -1.527525232 + -1 = -2.527525232 m = -2.527525232 Simplifying m = -2.527525232Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.527525232, -2.527525232}
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