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Simplifying m2 + 10 = 15m + -35 Reorder the terms: 10 + m2 = 15m + -35 Reorder the terms: 10 + m2 = -35 + 15m Solving 10 + m2 = -35 + 15m Solving for variable 'm'. Reorder the terms: 10 + 35 + -15m + m2 = -35 + 15m + 35 + -15m Combine like terms: 10 + 35 = 45 45 + -15m + m2 = -35 + 15m + 35 + -15m Reorder the terms: 45 + -15m + m2 = -35 + 35 + 15m + -15m Combine like terms: -35 + 35 = 0 45 + -15m + m2 = 0 + 15m + -15m 45 + -15m + m2 = 15m + -15m Combine like terms: 15m + -15m = 0 45 + -15m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -15m + -45 + m2 = 0 + -45 Reorder the terms: 45 + -45 + -15m + m2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -15m + m2 = 0 + -45 -15m + m2 = 0 + -45 Combine like terms: 0 + -45 = -45 -15m + m2 = -45 The m term is -15m. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15m + 56.25 + m2 = -45 + 56.25 Reorder the terms: 56.25 + -15m + m2 = -45 + 56.25 Combine like terms: -45 + 56.25 = 11.25 56.25 + -15m + m2 = 11.25 Factor a perfect square on the left side: (m + -7.5)(m + -7.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (m + -7.5) equal to 3.354101966 and -3.354101966.Subproblem 1
m + -7.5 = 3.354101966 Simplifying m + -7.5 = 3.354101966 Reorder the terms: -7.5 + m = 3.354101966 Solving -7.5 + m = 3.354101966 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + m = 3.354101966 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = 3.354101966 + 7.5 m = 3.354101966 + 7.5 Combine like terms: 3.354101966 + 7.5 = 10.854101966 m = 10.854101966 Simplifying m = 10.854101966Subproblem 2
m + -7.5 = -3.354101966 Simplifying m + -7.5 = -3.354101966 Reorder the terms: -7.5 + m = -3.354101966 Solving -7.5 + m = -3.354101966 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + m = -3.354101966 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = -3.354101966 + 7.5 m = -3.354101966 + 7.5 Combine like terms: -3.354101966 + 7.5 = 4.145898034 m = 4.145898034 Simplifying m = 4.145898034Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.854101966, 4.145898034}
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