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Simplifying 2m2 + -1m2 + -12m + 3m + -7 = 0 Reorder the terms: -7 + -12m + 3m + 2m2 + -1m2 = 0 Combine like terms: -12m + 3m = -9m -7 + -9m + 2m2 + -1m2 = 0 Combine like terms: 2m2 + -1m2 = 1m2 -7 + -9m + 1m2 = 0 Solving -7 + -9m + 1m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -9m + 7 + m2 = 0 + 7 Reorder the terms: -7 + 7 + -9m + m2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9m + m2 = 0 + 7 -9m + m2 = 0 + 7 Combine like terms: 0 + 7 = 7 -9m + m2 = 7 The m term is -9m. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9m + 20.25 + m2 = 7 + 20.25 Reorder the terms: 20.25 + -9m + m2 = 7 + 20.25 Combine like terms: 7 + 20.25 = 27.25 20.25 + -9m + m2 = 27.25 Factor a perfect square on the left side: (m + -4.5)(m + -4.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (m + -4.5) equal to 5.220153254 and -5.220153254.Subproblem 1
m + -4.5 = 5.220153254 Simplifying m + -4.5 = 5.220153254 Reorder the terms: -4.5 + m = 5.220153254 Solving -4.5 + m = 5.220153254 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = 5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = 5.220153254 + 4.5 m = 5.220153254 + 4.5 Combine like terms: 5.220153254 + 4.5 = 9.720153254 m = 9.720153254 Simplifying m = 9.720153254Subproblem 2
m + -4.5 = -5.220153254 Simplifying m + -4.5 = -5.220153254 Reorder the terms: -4.5 + m = -5.220153254 Solving -4.5 + m = -5.220153254 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = -5.220153254 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = -5.220153254 + 4.5 m = -5.220153254 + 4.5 Combine like terms: -5.220153254 + 4.5 = -0.720153254 m = -0.720153254 Simplifying m = -0.720153254Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.720153254, -0.720153254}
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