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Simplifying 41 + -2(m + 1) * m = 0 Reorder the terms: 41 + -2(1 + m) * m = 0 Reorder the terms for easier multiplication: 41 + -2m(1 + m) = 0 41 + (1 * -2m + m * -2m) = 0 41 + (-2m + -2m2) = 0 Solving 41 + -2m + -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'. -20.5 + m + m2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + m + 20.5 + m2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + m + m2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + m + m2 = 0 + 20.5 m + m2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 m + m2 = 20.5 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + m2 = 20.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 20.5 + 0.25 Combine like terms: 20.5 + 0.25 = 20.75 1.25 + m2 = 20.75 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 20.75 Calculate the square root of the right side: 4.55521679 Break this problem into two subproblems by setting (m + 0.5) equal to 4.55521679 and -4.55521679.Subproblem 1
m + 0.5 = 4.55521679 Simplifying m + 0.5 = 4.55521679 Reorder the terms: 0.5 + m = 4.55521679 Solving 0.5 + m = 4.55521679 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 4.55521679 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 4.55521679 + -0.5 m = 4.55521679 + -0.5 Combine like terms: 4.55521679 + -0.5 = 4.05521679 m = 4.05521679 Simplifying m = 4.05521679Subproblem 2
m + 0.5 = -4.55521679 Simplifying m + 0.5 = -4.55521679 Reorder the terms: 0.5 + m = -4.55521679 Solving 0.5 + m = -4.55521679 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -4.55521679 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -4.55521679 + -0.5 m = -4.55521679 + -0.5 Combine like terms: -4.55521679 + -0.5 = -5.05521679 m = -5.05521679 Simplifying m = -5.05521679Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.05521679, -5.05521679}
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