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Simplifying 6m(m + -4) = m + -15 Reorder the terms: 6m(-4 + m) = m + -15 (-4 * 6m + m * 6m) = m + -15 (-24m + 6m2) = m + -15 Reorder the terms: -24m + 6m2 = -15 + m Solving -24m + 6m2 = -15 + m Solving for variable 'm'. Reorder the terms: 15 + -24m + -1m + 6m2 = -15 + m + 15 + -1m Combine like terms: -24m + -1m = -25m 15 + -25m + 6m2 = -15 + m + 15 + -1m Reorder the terms: 15 + -25m + 6m2 = -15 + 15 + m + -1m Combine like terms: -15 + 15 = 0 15 + -25m + 6m2 = 0 + m + -1m 15 + -25m + 6m2 = m + -1m Combine like terms: m + -1m = 0 15 + -25m + 6m2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + -4.166666667m + m2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -4.166666667m + -2.5 + m2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -4.166666667m + m2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -4.166666667m + m2 = 0 + -2.5 -4.166666667m + m2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -4.166666667m + m2 = -2.5 The m term is -4.166666667m. Take half its coefficient (-2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. -4.166666667m + 4.340277781 + m2 = -2.5 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667m + m2 = -2.5 + 4.340277781 Combine like terms: -2.5 + 4.340277781 = 1.840277781 4.340277781 + -4.166666667m + m2 = 1.840277781 Factor a perfect square on the left side: (m + -2.083333334)(m + -2.083333334) = 1.840277781 Calculate the square root of the right side: 1.356568384 Break this problem into two subproblems by setting (m + -2.083333334) equal to 1.356568384 and -1.356568384.Subproblem 1
m + -2.083333334 = 1.356568384 Simplifying m + -2.083333334 = 1.356568384 Reorder the terms: -2.083333334 + m = 1.356568384 Solving -2.083333334 + m = 1.356568384 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + m = 1.356568384 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + m = 1.356568384 + 2.083333334 m = 1.356568384 + 2.083333334 Combine like terms: 1.356568384 + 2.083333334 = 3.439901718 m = 3.439901718 Simplifying m = 3.439901718Subproblem 2
m + -2.083333334 = -1.356568384 Simplifying m + -2.083333334 = -1.356568384 Reorder the terms: -2.083333334 + m = -1.356568384 Solving -2.083333334 + m = -1.356568384 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + m = -1.356568384 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + m = -1.356568384 + 2.083333334 m = -1.356568384 + 2.083333334 Combine like terms: -1.356568384 + 2.083333334 = 0.72676495 m = 0.72676495 Simplifying m = 0.72676495Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.439901718, 0.72676495}
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