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Simplifying -9m2 + -15m + 6 = -3m + -10m2 Reorder the terms: 6 + -15m + -9m2 = -3m + -10m2 Solving 6 + -15m + -9m2 = -3m + -10m2 Solving for variable 'm'. Reorder the terms: 6 + -15m + 3m + -9m2 + 10m2 = -3m + -10m2 + 3m + 10m2 Combine like terms: -15m + 3m = -12m 6 + -12m + -9m2 + 10m2 = -3m + -10m2 + 3m + 10m2 Combine like terms: -9m2 + 10m2 = 1m2 6 + -12m + 1m2 = -3m + -10m2 + 3m + 10m2 Reorder the terms: 6 + -12m + 1m2 = -3m + 3m + -10m2 + 10m2 Combine like terms: -3m + 3m = 0 6 + -12m + 1m2 = 0 + -10m2 + 10m2 6 + -12m + 1m2 = -10m2 + 10m2 Combine like terms: -10m2 + 10m2 = 0 6 + -12m + 1m2 = 0 Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -12m + -6 + m2 = 0 + -6 Reorder the terms: 6 + -6 + -12m + m2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -12m + m2 = 0 + -6 -12m + m2 = 0 + -6 Combine like terms: 0 + -6 = -6 -12m + m2 = -6 The m term is -12m. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12m + 36 + m2 = -6 + 36 Reorder the terms: 36 + -12m + m2 = -6 + 36 Combine like terms: -6 + 36 = 30 36 + -12m + m2 = 30 Factor a perfect square on the left side: (m + -6)(m + -6) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (m + -6) equal to 5.477225575 and -5.477225575.Subproblem 1
m + -6 = 5.477225575 Simplifying m + -6 = 5.477225575 Reorder the terms: -6 + m = 5.477225575 Solving -6 + m = 5.477225575 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + m = 5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + m = 5.477225575 + 6 m = 5.477225575 + 6 Combine like terms: 5.477225575 + 6 = 11.477225575 m = 11.477225575 Simplifying m = 11.477225575Subproblem 2
m + -6 = -5.477225575 Simplifying m + -6 = -5.477225575 Reorder the terms: -6 + m = -5.477225575 Solving -6 + m = -5.477225575 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + m = -5.477225575 + 6 Combine like terms: -6 + 6 = 0 0 + m = -5.477225575 + 6 m = -5.477225575 + 6 Combine like terms: -5.477225575 + 6 = 0.522774425 m = 0.522774425 Simplifying m = 0.522774425Solution
The solution to the problem is based on the solutions from the subproblems. m = {11.477225575, 0.522774425}
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