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Simplifying -9m2 + -9m + 5 = 0 Reorder the terms: 5 + -9m + -9m2 = 0 Solving 5 + -9m + -9m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.5555555556 + m + m2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + m + 0.5555555556 + m2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + m + m2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + m + m2 = 0 + 0.5555555556 m + m2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 m + m2 = 0.5555555556 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 = 0.5555555556 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 0.5555555556 + 0.25 Combine like terms: 0.5555555556 + 0.25 = 0.8055555556 1.25 + m2 = 0.8055555556 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 0.8055555556 Calculate the square root of the right side: 0.897527468 Break this problem into two subproblems by setting (m + 0.5) equal to 0.897527468 and -0.897527468.Subproblem 1
m + 0.5 = 0.897527468 Simplifying m + 0.5 = 0.897527468 Reorder the terms: 0.5 + m = 0.897527468 Solving 0.5 + m = 0.897527468 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 = 0.897527468 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 0.897527468 + -0.5 m = 0.897527468 + -0.5 Combine like terms: 0.897527468 + -0.5 = 0.397527468 m = 0.397527468 Simplifying m = 0.397527468Subproblem 2
m + 0.5 = -0.897527468 Simplifying m + 0.5 = -0.897527468 Reorder the terms: 0.5 + m = -0.897527468 Solving 0.5 + m = -0.897527468 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 = -0.897527468 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -0.897527468 + -0.5 m = -0.897527468 + -0.5 Combine like terms: -0.897527468 + -0.5 = -1.397527468 m = -1.397527468 Simplifying m = -1.397527468Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.397527468, -1.397527468}
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