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Simplifying 7m2 + -41m + -30 = 0 Reorder the terms: -30 + -41m + 7m2 = 0 Solving -30 + -41m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.285714286 + -5.857142857m + m2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + -5.857142857m + 4.285714286 + m2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + -5.857142857m + m2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + -5.857142857m + m2 = 0 + 4.285714286 -5.857142857m + m2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 -5.857142857m + m2 = 4.285714286 The m term is -5.857142857m. Take half its coefficient (-2.928571429). Square it (8.576530615) and add it to both sides. Add '8.576530615' to each side of the equation. -5.857142857m + 8.576530615 + m2 = 4.285714286 + 8.576530615 Reorder the terms: 8.576530615 + -5.857142857m + m2 = 4.285714286 + 8.576530615 Combine like terms: 4.285714286 + 8.576530615 = 12.862244901 8.576530615 + -5.857142857m + m2 = 12.862244901 Factor a perfect square on the left side: (m + -2.928571429)(m + -2.928571429) = 12.862244901 Calculate the square root of the right side: 3.586397203 Break this problem into two subproblems by setting (m + -2.928571429) equal to 3.586397203 and -3.586397203.Subproblem 1
m + -2.928571429 = 3.586397203 Simplifying m + -2.928571429 = 3.586397203 Reorder the terms: -2.928571429 + m = 3.586397203 Solving -2.928571429 + m = 3.586397203 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.928571429' to each side of the equation. -2.928571429 + 2.928571429 + m = 3.586397203 + 2.928571429 Combine like terms: -2.928571429 + 2.928571429 = 0.000000000 0.000000000 + m = 3.586397203 + 2.928571429 m = 3.586397203 + 2.928571429 Combine like terms: 3.586397203 + 2.928571429 = 6.514968632 m = 6.514968632 Simplifying m = 6.514968632Subproblem 2
m + -2.928571429 = -3.586397203 Simplifying m + -2.928571429 = -3.586397203 Reorder the terms: -2.928571429 + m = -3.586397203 Solving -2.928571429 + m = -3.586397203 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.928571429' to each side of the equation. -2.928571429 + 2.928571429 + m = -3.586397203 + 2.928571429 Combine like terms: -2.928571429 + 2.928571429 = 0.000000000 0.000000000 + m = -3.586397203 + 2.928571429 m = -3.586397203 + 2.928571429 Combine like terms: -3.586397203 + 2.928571429 = -0.657825774 m = -0.657825774 Simplifying m = -0.657825774Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.514968632, -0.657825774}
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