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Simplifying 3m2 + -33m + 28 = 0 Reorder the terms: 28 + -33m + 3m2 = 0 Solving 28 + -33m + 3m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 9.333333333 + -11m + m2 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + -11m + -9.333333333 + m2 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + -11m + m2 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + -11m + m2 = 0 + -9.333333333 -11m + m2 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 -11m + m2 = -9.333333333 The m term is -11m. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11m + 30.25 + m2 = -9.333333333 + 30.25 Reorder the terms: 30.25 + -11m + m2 = -9.333333333 + 30.25 Combine like terms: -9.333333333 + 30.25 = 20.916666667 30.25 + -11m + m2 = 20.916666667 Factor a perfect square on the left side: (m + -5.5)(m + -5.5) = 20.916666667 Calculate the square root of the right side: 4.573474245 Break this problem into two subproblems by setting (m + -5.5) equal to 4.573474245 and -4.573474245.Subproblem 1
m + -5.5 = 4.573474245 Simplifying m + -5.5 = 4.573474245 Reorder the terms: -5.5 + m = 4.573474245 Solving -5.5 + m = 4.573474245 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m = 4.573474245 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = 4.573474245 + 5.5 m = 4.573474245 + 5.5 Combine like terms: 4.573474245 + 5.5 = 10.073474245 m = 10.073474245 Simplifying m = 10.073474245Subproblem 2
m + -5.5 = -4.573474245 Simplifying m + -5.5 = -4.573474245 Reorder the terms: -5.5 + m = -4.573474245 Solving -5.5 + m = -4.573474245 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + m = -4.573474245 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + m = -4.573474245 + 5.5 m = -4.573474245 + 5.5 Combine like terms: -4.573474245 + 5.5 = 0.926525755 m = 0.926525755 Simplifying m = 0.926525755Solution
The solution to the problem is based on the solutions from the subproblems. m = {10.073474245, 0.926525755}
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