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Simplifying m2 = -7m + 12 Reorder the terms: m2 = 12 + -7m Solving m2 = 12 + -7m Solving for variable 'm'. Reorder the terms: -12 + 7m + m2 = 12 + -7m + -12 + 7m Reorder the terms: -12 + 7m + m2 = 12 + -12 + -7m + 7m Combine like terms: 12 + -12 = 0 -12 + 7m + m2 = 0 + -7m + 7m -12 + 7m + m2 = -7m + 7m Combine like terms: -7m + 7m = 0 -12 + 7m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 7m + 12 + m2 = 0 + 12 Reorder the terms: -12 + 12 + 7m + m2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 7m + m2 = 0 + 12 7m + m2 = 0 + 12 Combine like terms: 0 + 12 = 12 7m + m2 = 12 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = 12 + 12.25 Reorder the terms: 12.25 + 7m + m2 = 12 + 12.25 Combine like terms: 12 + 12.25 = 24.25 12.25 + 7m + m2 = 24.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (m + 3.5) equal to 4.924428901 and -4.924428901.Subproblem 1
m + 3.5 = 4.924428901 Simplifying m + 3.5 = 4.924428901 Reorder the terms: 3.5 + m = 4.924428901 Solving 3.5 + m = 4.924428901 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 4.924428901 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 4.924428901 + -3.5 m = 4.924428901 + -3.5 Combine like terms: 4.924428901 + -3.5 = 1.424428901 m = 1.424428901 Simplifying m = 1.424428901Subproblem 2
m + 3.5 = -4.924428901 Simplifying m + 3.5 = -4.924428901 Reorder the terms: 3.5 + m = -4.924428901 Solving 3.5 + m = -4.924428901 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -4.924428901 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -4.924428901 + -3.5 m = -4.924428901 + -3.5 Combine like terms: -4.924428901 + -3.5 = -8.424428901 m = -8.424428901 Simplifying m = -8.424428901Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.424428901, -8.424428901}
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