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Simplifying 3m(2m + -1) + 5 = 6(m + 11) Reorder the terms: 3m(-1 + 2m) + 5 = 6(m + 11) (-1 * 3m + 2m * 3m) + 5 = 6(m + 11) (-3m + 6m2) + 5 = 6(m + 11) Reorder the terms: 5 + -3m + 6m2 = 6(m + 11) Reorder the terms: 5 + -3m + 6m2 = 6(11 + m) 5 + -3m + 6m2 = (11 * 6 + m * 6) 5 + -3m + 6m2 = (66 + 6m) Solving 5 + -3m + 6m2 = 66 + 6m Solving for variable 'm'. Reorder the terms: 5 + -66 + -3m + -6m + 6m2 = 66 + 6m + -66 + -6m Combine like terms: 5 + -66 = -61 -61 + -3m + -6m + 6m2 = 66 + 6m + -66 + -6m Combine like terms: -3m + -6m = -9m -61 + -9m + 6m2 = 66 + 6m + -66 + -6m Reorder the terms: -61 + -9m + 6m2 = 66 + -66 + 6m + -6m Combine like terms: 66 + -66 = 0 -61 + -9m + 6m2 = 0 + 6m + -6m -61 + -9m + 6m2 = 6m + -6m Combine like terms: 6m + -6m = 0 -61 + -9m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -10.16666667 + -1.5m + m2 = 0 Move the constant term to the right: Add '10.16666667' to each side of the equation. -10.16666667 + -1.5m + 10.16666667 + m2 = 0 + 10.16666667 Reorder the terms: -10.16666667 + 10.16666667 + -1.5m + m2 = 0 + 10.16666667 Combine like terms: -10.16666667 + 10.16666667 = 0.00000000 0.00000000 + -1.5m + m2 = 0 + 10.16666667 -1.5m + m2 = 0 + 10.16666667 Combine like terms: 0 + 10.16666667 = 10.16666667 -1.5m + m2 = 10.16666667 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 = 10.16666667 + 0.5625 Reorder the terms: 0.5625 + -1.5m + m2 = 10.16666667 + 0.5625 Combine like terms: 10.16666667 + 0.5625 = 10.72916667 0.5625 + -1.5m + m2 = 10.72916667 Factor a perfect square on the left side: (m + -0.75)(m + -0.75) = 10.72916667 Calculate the square root of the right side: 3.275540668 Break this problem into two subproblems by setting (m + -0.75) equal to 3.275540668 and -3.275540668.Subproblem 1
m + -0.75 = 3.275540668 Simplifying m + -0.75 = 3.275540668 Reorder the terms: -0.75 + m = 3.275540668 Solving -0.75 + m = 3.275540668 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 = 3.275540668 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = 3.275540668 + 0.75 m = 3.275540668 + 0.75 Combine like terms: 3.275540668 + 0.75 = 4.025540668 m = 4.025540668 Simplifying m = 4.025540668Subproblem 2
m + -0.75 = -3.275540668 Simplifying m + -0.75 = -3.275540668 Reorder the terms: -0.75 + m = -3.275540668 Solving -0.75 + m = -3.275540668 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 = -3.275540668 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = -3.275540668 + 0.75 m = -3.275540668 + 0.75 Combine like terms: -3.275540668 + 0.75 = -2.525540668 m = -2.525540668 Simplifying m = -2.525540668Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.025540668, -2.525540668}
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