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Simplifying m2 = 15m + 50 Reorder the terms: m2 = 50 + 15m Solving m2 = 50 + 15m Solving for variable 'm'. Reorder the terms: -50 + -15m + m2 = 50 + 15m + -50 + -15m Reorder the terms: -50 + -15m + m2 = 50 + -50 + 15m + -15m Combine like terms: 50 + -50 = 0 -50 + -15m + m2 = 0 + 15m + -15m -50 + -15m + m2 = 15m + -15m Combine like terms: 15m + -15m = 0 -50 + -15m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -15m + 50 + m2 = 0 + 50 Reorder the terms: -50 + 50 + -15m + m2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -15m + m2 = 0 + 50 -15m + m2 = 0 + 50 Combine like terms: 0 + 50 = 50 -15m + m2 = 50 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 = 50 + 56.25 Reorder the terms: 56.25 + -15m + m2 = 50 + 56.25 Combine like terms: 50 + 56.25 = 106.25 56.25 + -15m + m2 = 106.25 Factor a perfect square on the left side: (m + -7.5)(m + -7.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (m + -7.5) equal to 10.307764064 and -10.307764064.Subproblem 1
m + -7.5 = 10.307764064 Simplifying m + -7.5 = 10.307764064 Reorder the terms: -7.5 + m = 10.307764064 Solving -7.5 + m = 10.307764064 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 = 10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = 10.307764064 + 7.5 m = 10.307764064 + 7.5 Combine like terms: 10.307764064 + 7.5 = 17.807764064 m = 17.807764064 Simplifying m = 17.807764064Subproblem 2
m + -7.5 = -10.307764064 Simplifying m + -7.5 = -10.307764064 Reorder the terms: -7.5 + m = -10.307764064 Solving -7.5 + m = -10.307764064 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 = -10.307764064 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + m = -10.307764064 + 7.5 m = -10.307764064 + 7.5 Combine like terms: -10.307764064 + 7.5 = -2.807764064 m = -2.807764064 Simplifying m = -2.807764064Solution
The solution to the problem is based on the solutions from the subproblems. m = {17.807764064, -2.807764064}
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