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Simplifying -9m2 + 11 + -2 + 4m2 + -8m + 7 = 0 Reorder the terms: 11 + -2 + 7 + -8m + -9m2 + 4m2 = 0 Combine like terms: 11 + -2 = 9 9 + 7 + -8m + -9m2 + 4m2 = 0 Combine like terms: 9 + 7 = 16 16 + -8m + -9m2 + 4m2 = 0 Combine like terms: -9m2 + 4m2 = -5m2 16 + -8m + -5m2 = 0 Solving 16 + -8m + -5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.2 + 1.6m + m2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 1.6m + 3.2 + m2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 1.6m + m2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 1.6m + m2 = 0 + 3.2 1.6m + m2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 1.6m + m2 = 3.2 The m term is 1.6m. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6m + 0.64 + m2 = 3.2 + 0.64 Reorder the terms: 0.64 + 1.6m + m2 = 3.2 + 0.64 Combine like terms: 3.2 + 0.64 = 3.84 0.64 + 1.6m + m2 = 3.84 Factor a perfect square on the left side: (m + 0.8)(m + 0.8) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (m + 0.8) equal to 1.959591794 and -1.959591794.Subproblem 1
m + 0.8 = 1.959591794 Simplifying m + 0.8 = 1.959591794 Reorder the terms: 0.8 + m = 1.959591794 Solving 0.8 + m = 1.959591794 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + m = 1.959591794 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + m = 1.959591794 + -0.8 m = 1.959591794 + -0.8 Combine like terms: 1.959591794 + -0.8 = 1.159591794 m = 1.159591794 Simplifying m = 1.159591794Subproblem 2
m + 0.8 = -1.959591794 Simplifying m + 0.8 = -1.959591794 Reorder the terms: 0.8 + m = -1.959591794 Solving 0.8 + m = -1.959591794 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + m = -1.959591794 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + m = -1.959591794 + -0.8 m = -1.959591794 + -0.8 Combine like terms: -1.959591794 + -0.8 = -2.759591794 m = -2.759591794 Simplifying m = -2.759591794Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.159591794, -2.759591794}
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