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Simplifying (10m2 + -7m + 2) + -1(3m2 + -2m + 5) = 0 Reorder the terms: (2 + -7m + 10m2) + -1(3m2 + -2m + 5) = 0 Remove parenthesis around (2 + -7m + 10m2) 2 + -7m + 10m2 + -1(3m2 + -2m + 5) = 0 Reorder the terms: 2 + -7m + 10m2 + -1(5 + -2m + 3m2) = 0 2 + -7m + 10m2 + (5 * -1 + -2m * -1 + 3m2 * -1) = 0 2 + -7m + 10m2 + (-5 + 2m + -3m2) = 0 Reorder the terms: 2 + -5 + -7m + 2m + 10m2 + -3m2 = 0 Combine like terms: 2 + -5 = -3 -3 + -7m + 2m + 10m2 + -3m2 = 0 Combine like terms: -7m + 2m = -5m -3 + -5m + 10m2 + -3m2 = 0 Combine like terms: 10m2 + -3m2 = 7m2 -3 + -5m + 7m2 = 0 Solving -3 + -5m + 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'. -0.4285714286 + -0.7142857143m + m2 = 0 Move the constant term to the right: Add '0.4285714286' to each side of the equation. -0.4285714286 + -0.7142857143m + 0.4285714286 + m2 = 0 + 0.4285714286 Reorder the terms: -0.4285714286 + 0.4285714286 + -0.7142857143m + m2 = 0 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + -0.7142857143m + m2 = 0 + 0.4285714286 -0.7142857143m + m2 = 0 + 0.4285714286 Combine like terms: 0 + 0.4285714286 = 0.4285714286 -0.7142857143m + m2 = 0.4285714286 The m term is -0.7142857143m. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143m + 0.1275510204 + m2 = 0.4285714286 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143m + m2 = 0.4285714286 + 0.1275510204 Combine like terms: 0.4285714286 + 0.1275510204 = 0.556122449 0.1275510204 + -0.7142857143m + m2 = 0.556122449 Factor a perfect square on the left side: (m + -0.3571428572)(m + -0.3571428572) = 0.556122449 Calculate the square root of the right side: 0.745736179 Break this problem into two subproblems by setting (m + -0.3571428572) equal to 0.745736179 and -0.745736179.Subproblem 1
m + -0.3571428572 = 0.745736179 Simplifying m + -0.3571428572 = 0.745736179 Reorder the terms: -0.3571428572 + m = 0.745736179 Solving -0.3571428572 + m = 0.745736179 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + m = 0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + m = 0.745736179 + 0.3571428572 m = 0.745736179 + 0.3571428572 Combine like terms: 0.745736179 + 0.3571428572 = 1.1028790362 m = 1.1028790362 Simplifying m = 1.1028790362Subproblem 2
m + -0.3571428572 = -0.745736179 Simplifying m + -0.3571428572 = -0.745736179 Reorder the terms: -0.3571428572 + m = -0.745736179 Solving -0.3571428572 + m = -0.745736179 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + m = -0.745736179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + m = -0.745736179 + 0.3571428572 m = -0.745736179 + 0.3571428572 Combine like terms: -0.745736179 + 0.3571428572 = -0.3885933218 m = -0.3885933218 Simplifying m = -0.3885933218Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.1028790362, -0.3885933218}
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