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Simplifying 3m + -6 = m2 + -5m Reorder the terms: -6 + 3m = m2 + -5m Reorder the terms: -6 + 3m = -5m + m2 Solving -6 + 3m = -5m + m2 Solving for variable 'm'. Combine like terms: 3m + 5m = 8m -6 + 8m + -1m2 = -5m + m2 + 5m + -1m2 Reorder the terms: -6 + 8m + -1m2 = -5m + 5m + m2 + -1m2 Combine like terms: -5m + 5m = 0 -6 + 8m + -1m2 = 0 + m2 + -1m2 -6 + 8m + -1m2 = m2 + -1m2 Combine like terms: m2 + -1m2 = 0 -6 + 8m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -8m + m2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8m + -6 + m2 = 0 + -6 Reorder the terms: 6 + -6 + -8m + m2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8m + m2 = 0 + -6 -8m + m2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8m + m2 = -6 The m term is -8m. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8m + 16 + m2 = -6 + 16 Reorder the terms: 16 + -8m + m2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + -8m + m2 = 10 Factor a perfect square on the left side: (m + -4)(m + -4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (m + -4) equal to 3.16227766 and -3.16227766.Subproblem 1
m + -4 = 3.16227766 Simplifying m + -4 = 3.16227766 Reorder the terms: -4 + m = 3.16227766 Solving -4 + m = 3.16227766 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = 3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + m = 3.16227766 + 4 m = 3.16227766 + 4 Combine like terms: 3.16227766 + 4 = 7.16227766 m = 7.16227766 Simplifying m = 7.16227766Subproblem 2
m + -4 = -3.16227766 Simplifying m + -4 = -3.16227766 Reorder the terms: -4 + m = -3.16227766 Solving -4 + m = -3.16227766 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + m = -3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + m = -3.16227766 + 4 m = -3.16227766 + 4 Combine like terms: -3.16227766 + 4 = 0.83772234 m = 0.83772234 Simplifying m = 0.83772234Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.16227766, 0.83772234}
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