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Simplifying -8(1 + 9m) + 4m(7m + 3) = 1 (1 * -8 + 9m * -8) + 4m(7m + 3) = 1 (-8 + -72m) + 4m(7m + 3) = 1 Reorder the terms: -8 + -72m + 4m(3 + 7m) = 1 -8 + -72m + (3 * 4m + 7m * 4m) = 1 -8 + -72m + (12m + 28m2) = 1 Combine like terms: -72m + 12m = -60m -8 + -60m + 28m2 = 1 Solving -8 + -60m + 28m2 = 1 Solving for variable 'm'. Reorder the terms: -8 + -1 + -60m + 28m2 = 1 + -1 Combine like terms: -8 + -1 = -9 -9 + -60m + 28m2 = 1 + -1 Combine like terms: 1 + -1 = 0 -9 + -60m + 28m2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -0.3214285714 + -2.142857143m + m2 = 0 Move the constant term to the right: Add '0.3214285714' to each side of the equation. -0.3214285714 + -2.142857143m + 0.3214285714 + m2 = 0 + 0.3214285714 Reorder the terms: -0.3214285714 + 0.3214285714 + -2.142857143m + m2 = 0 + 0.3214285714 Combine like terms: -0.3214285714 + 0.3214285714 = 0.0000000000 0.0000000000 + -2.142857143m + m2 = 0 + 0.3214285714 -2.142857143m + m2 = 0 + 0.3214285714 Combine like terms: 0 + 0.3214285714 = 0.3214285714 -2.142857143m + m2 = 0.3214285714 The m term is -2.142857143m. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143m + 1.147959185 + m2 = 0.3214285714 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143m + m2 = 0.3214285714 + 1.147959185 Combine like terms: 0.3214285714 + 1.147959185 = 1.4693877564 1.147959185 + -2.142857143m + m2 = 1.4693877564 Factor a perfect square on the left side: (m + -1.071428572)(m + -1.071428572) = 1.4693877564 Calculate the square root of the right side: 1.212183054 Break this problem into two subproblems by setting (m + -1.071428572) equal to 1.212183054 and -1.212183054.Subproblem 1
m + -1.071428572 = 1.212183054 Simplifying m + -1.071428572 = 1.212183054 Reorder the terms: -1.071428572 + m = 1.212183054 Solving -1.071428572 + m = 1.212183054 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + m = 1.212183054 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + m = 1.212183054 + 1.071428572 m = 1.212183054 + 1.071428572 Combine like terms: 1.212183054 + 1.071428572 = 2.283611626 m = 2.283611626 Simplifying m = 2.283611626Subproblem 2
m + -1.071428572 = -1.212183054 Simplifying m + -1.071428572 = -1.212183054 Reorder the terms: -1.071428572 + m = -1.212183054 Solving -1.071428572 + m = -1.212183054 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + m = -1.212183054 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + m = -1.212183054 + 1.071428572 m = -1.212183054 + 1.071428572 Combine like terms: -1.212183054 + 1.071428572 = -0.140754482 m = -0.140754482 Simplifying m = -0.140754482Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.283611626, -0.140754482}
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