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Simplifying 9M2 = 90M + -49 Reorder the terms: 9M2 = -49 + 90M Solving 9M2 = -49 + 90M Solving for variable 'M'. Reorder the terms: 49 + -90M + 9M2 = -49 + 90M + 49 + -90M Reorder the terms: 49 + -90M + 9M2 = -49 + 49 + 90M + -90M Combine like terms: -49 + 49 = 0 49 + -90M + 9M2 = 0 + 90M + -90M 49 + -90M + 9M2 = 90M + -90M Combine like terms: 90M + -90M = 0 49 + -90M + 9M2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 5.444444444 + -10M + M2 = 0 Move the constant term to the right: Add '-5.444444444' to each side of the equation. 5.444444444 + -10M + -5.444444444 + M2 = 0 + -5.444444444 Reorder the terms: 5.444444444 + -5.444444444 + -10M + M2 = 0 + -5.444444444 Combine like terms: 5.444444444 + -5.444444444 = 0.000000000 0.000000000 + -10M + M2 = 0 + -5.444444444 -10M + M2 = 0 + -5.444444444 Combine like terms: 0 + -5.444444444 = -5.444444444 -10M + M2 = -5.444444444 The M term is -10M. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10M + 25 + M2 = -5.444444444 + 25 Reorder the terms: 25 + -10M + M2 = -5.444444444 + 25 Combine like terms: -5.444444444 + 25 = 19.555555556 25 + -10M + M2 = 19.555555556 Factor a perfect square on the left side: (M + -5)(M + -5) = 19.555555556 Calculate the square root of the right side: 4.422166387 Break this problem into two subproblems by setting (M + -5) equal to 4.422166387 and -4.422166387.Subproblem 1
M + -5 = 4.422166387 Simplifying M + -5 = 4.422166387 Reorder the terms: -5 + M = 4.422166387 Solving -5 + M = 4.422166387 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + M = 4.422166387 + 5 Combine like terms: -5 + 5 = 0 0 + M = 4.422166387 + 5 M = 4.422166387 + 5 Combine like terms: 4.422166387 + 5 = 9.422166387 M = 9.422166387 Simplifying M = 9.422166387Subproblem 2
M + -5 = -4.422166387 Simplifying M + -5 = -4.422166387 Reorder the terms: -5 + M = -4.422166387 Solving -5 + M = -4.422166387 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + M = -4.422166387 + 5 Combine like terms: -5 + 5 = 0 0 + M = -4.422166387 + 5 M = -4.422166387 + 5 Combine like terms: -4.422166387 + 5 = 0.577833613 M = 0.577833613 Simplifying M = 0.577833613Solution
The solution to the problem is based on the solutions from the subproblems. M = {9.422166387, 0.577833613}
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