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Simplifying 7m2 + m = 11 Reorder the terms: m + 7m2 = 11 Solving m + 7m2 = 11 Solving for variable 'm'. Reorder the terms: -11 + m + 7m2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + m + 7m2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.571428571 + 0.1428571429m + m2 = 0 Move the constant term to the right: Add '1.571428571' to each side of the equation. -1.571428571 + 0.1428571429m + 1.571428571 + m2 = 0 + 1.571428571 Reorder the terms: -1.571428571 + 1.571428571 + 0.1428571429m + m2 = 0 + 1.571428571 Combine like terms: -1.571428571 + 1.571428571 = 0.000000000 0.000000000 + 0.1428571429m + m2 = 0 + 1.571428571 0.1428571429m + m2 = 0 + 1.571428571 Combine like terms: 0 + 1.571428571 = 1.571428571 0.1428571429m + m2 = 1.571428571 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. 0.1428571429m + 0.25 + m2 = 1.571428571 + 0.25 Reorder the terms: 0.25 + 0.1428571429m + m2 = 1.571428571 + 0.25 Combine like terms: 1.571428571 + 0.25 = 1.821428571 0.25 + 0.1428571429m + m2 = 1.821428571 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 1.821428571 Calculate the square root of the right side: 1.349603116 Break this problem into two subproblems by setting (m + 0.5) equal to 1.349603116 and -1.349603116.Subproblem 1
m + 0.5 = 1.349603116 Simplifying m + 0.5 = 1.349603116 Reorder the terms: 0.5 + m = 1.349603116 Solving 0.5 + m = 1.349603116 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 = 1.349603116 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.349603116 + -0.5 m = 1.349603116 + -0.5 Combine like terms: 1.349603116 + -0.5 = 0.849603116 m = 0.849603116 Simplifying m = 0.849603116Subproblem 2
m + 0.5 = -1.349603116 Simplifying m + 0.5 = -1.349603116 Reorder the terms: 0.5 + m = -1.349603116 Solving 0.5 + m = -1.349603116 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 = -1.349603116 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.349603116 + -0.5 m = -1.349603116 + -0.5 Combine like terms: -1.349603116 + -0.5 = -1.849603116 m = -1.849603116 Simplifying m = -1.849603116Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.849603116, -1.849603116}
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