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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 = -3m 6m + m + -4(1 + -3m) * m = 8 Reorder the terms for easier multiplication: 6m + m + -4m(1 + -3m) = 8 6m + m + (1 * -4m + -3m * -4m) = 8 6m + m + (-4m + 12m2) = 8 Combine like terms: 6m + m = 7m 7m + -4m + 12m2 = 8 Combine like terms: 7m + -4m = 3m 3m + 12m2 = 8 Solving 3m + 12m2 = 8 Solving for variable 'm'. Reorder the terms: -8 + 3m + 12m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 3m + 12m2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.6666666667 + 0.25m + m2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.25m + 0.6666666667 + m2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.25m + m2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.25m + m2 = 0 + 0.6666666667 0.25m + m2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.25m + m2 = 0.6666666667 The m term is 0.25m. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25m + 0.015625 + m2 = 0.6666666667 + 0.015625 Reorder the terms: 0.015625 + 0.25m + m2 = 0.6666666667 + 0.015625 Combine like terms: 0.6666666667 + 0.015625 = 0.6822916667 0.015625 + 0.25m + m2 = 0.6822916667 Factor a perfect square on the left side: (m + 0.125)(m + 0.125) = 0.6822916667 Calculate the square root of the right side: 0.826009483 Break this problem into two subproblems by setting (m + 0.125) equal to 0.826009483 and -0.826009483.Subproblem 1
m + 0.125 = 0.826009483 Simplifying m + 0.125 = 0.826009483 Reorder the terms: 0.125 + m = 0.826009483 Solving 0.125 + m = 0.826009483 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = 0.826009483 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = 0.826009483 + -0.125 m = 0.826009483 + -0.125 Combine like terms: 0.826009483 + -0.125 = 0.701009483 m = 0.701009483 Simplifying m = 0.701009483Subproblem 2
m + 0.125 = -0.826009483 Simplifying m + 0.125 = -0.826009483 Reorder the terms: 0.125 + m = -0.826009483 Solving 0.125 + m = -0.826009483 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + m = -0.826009483 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + m = -0.826009483 + -0.125 m = -0.826009483 + -0.125 Combine like terms: -0.826009483 + -0.125 = -0.951009483 m = -0.951009483 Simplifying m = -0.951009483Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.701009483, -0.951009483}
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