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Simplifying 2m2 + -1m + -2 + -21 = 0 Reorder the terms: -2 + -21 + -1m + 2m2 = 0 Combine like terms: -2 + -21 = -23 -23 + -1m + 2m2 = 0 Solving -23 + -1m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -0.5m + m2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -0.5m + 11.5 + m2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -0.5m + m2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -0.5m + m2 = 0 + 11.5 -0.5m + m2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -0.5m + m2 = 11.5 The m term is -0.5m. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5m + 0.0625 + m2 = 11.5 + 0.0625 Reorder the terms: 0.0625 + -0.5m + m2 = 11.5 + 0.0625 Combine like terms: 11.5 + 0.0625 = 11.5625 0.0625 + -0.5m + m2 = 11.5625 Factor a perfect square on the left side: (m + -0.25)(m + -0.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (m + -0.25) equal to 3.400367627 and -3.400367627.Subproblem 1
m + -0.25 = 3.400367627 Simplifying m + -0.25 = 3.400367627 Reorder the terms: -0.25 + m = 3.400367627 Solving -0.25 + m = 3.400367627 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + m = 3.400367627 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = 3.400367627 + 0.25 m = 3.400367627 + 0.25 Combine like terms: 3.400367627 + 0.25 = 3.650367627 m = 3.650367627 Simplifying m = 3.650367627Subproblem 2
m + -0.25 = -3.400367627 Simplifying m + -0.25 = -3.400367627 Reorder the terms: -0.25 + m = -3.400367627 Solving -0.25 + m = -3.400367627 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + m = -3.400367627 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = -3.400367627 + 0.25 m = -3.400367627 + 0.25 Combine like terms: -3.400367627 + 0.25 = -3.150367627 m = -3.150367627 Simplifying m = -3.150367627Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.650367627, -3.150367627}
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