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Simplifying (8m2 + 2m) + -1(-8m2 + -7m + 9) = 0 Reorder the terms: (2m + 8m2) + -1(-8m2 + -7m + 9) = 0 Remove parenthesis around (2m + 8m2) 2m + 8m2 + -1(-8m2 + -7m + 9) = 0 Reorder the terms: 2m + 8m2 + -1(9 + -7m + -8m2) = 0 2m + 8m2 + (9 * -1 + -7m * -1 + -8m2 * -1) = 0 2m + 8m2 + (-9 + 7m + 8m2) = 0 Reorder the terms: -9 + 2m + 7m + 8m2 + 8m2 = 0 Combine like terms: 2m + 7m = 9m -9 + 9m + 8m2 + 8m2 = 0 Combine like terms: 8m2 + 8m2 = 16m2 -9 + 9m + 16m2 = 0 Solving -9 + 9m + 16m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5625 + 0.5625m + m2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + 0.5625m + 0.5625 + m2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + 0.5625m + m2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + 0.5625m + m2 = 0 + 0.5625 0.5625m + m2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 0.5625m + m2 = 0.5625 The m term is 0.5625m. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625m + 0.0791015625 + m2 = 0.5625 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625m + m2 = 0.5625 + 0.0791015625 Combine like terms: 0.5625 + 0.0791015625 = 0.6416015625 0.0791015625 + 0.5625m + m2 = 0.6416015625 Factor a perfect square on the left side: (m + 0.28125)(m + 0.28125) = 0.6416015625 Calculate the square root of the right side: 0.801000351 Break this problem into two subproblems by setting (m + 0.28125) equal to 0.801000351 and -0.801000351.Subproblem 1
m + 0.28125 = 0.801000351 Simplifying m + 0.28125 = 0.801000351 Reorder the terms: 0.28125 + m = 0.801000351 Solving 0.28125 + m = 0.801000351 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + m = 0.801000351 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + m = 0.801000351 + -0.28125 m = 0.801000351 + -0.28125 Combine like terms: 0.801000351 + -0.28125 = 0.519750351 m = 0.519750351 Simplifying m = 0.519750351Subproblem 2
m + 0.28125 = -0.801000351 Simplifying m + 0.28125 = -0.801000351 Reorder the terms: 0.28125 + m = -0.801000351 Solving 0.28125 + m = -0.801000351 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + m = -0.801000351 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + m = -0.801000351 + -0.28125 m = -0.801000351 + -0.28125 Combine like terms: -0.801000351 + -0.28125 = -1.082250351 m = -1.082250351 Simplifying m = -1.082250351Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.519750351, -1.082250351}
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