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Simplifying [(8m2 + 4m + -7) + -1(2m2 + -5m + 2)] + -1(m2 + m + 1) = 0 Reorder the terms: [(-7 + 4m + 8m2) + -1(2m2 + -5m + 2)] + -1(m2 + m + 1) = 0 Remove parenthesis around (-7 + 4m + 8m2) [-7 + 4m + 8m2 + -1(2m2 + -5m + 2)] + -1(m2 + m + 1) = 0 Reorder the terms: [-7 + 4m + 8m2 + -1(2 + -5m + 2m2)] + -1(m2 + m + 1) = 0 [-7 + 4m + 8m2 + (2 * -1 + -5m * -1 + 2m2 * -1)] + -1(m2 + m + 1) = 0 [-7 + 4m + 8m2 + (-2 + 5m + -2m2)] + -1(m2 + m + 1) = 0 Reorder the terms: [-7 + -2 + 4m + 5m + 8m2 + -2m2] + -1(m2 + m + 1) = 0 Combine like terms: -7 + -2 = -9 [-9 + 4m + 5m + 8m2 + -2m2] + -1(m2 + m + 1) = 0 Combine like terms: 4m + 5m = 9m [-9 + 9m + 8m2 + -2m2] + -1(m2 + m + 1) = 0 Combine like terms: 8m2 + -2m2 = 6m2 [-9 + 9m + 6m2] + -1(m2 + m + 1) = 0 Remove brackets around [-9 + 9m + 6m2] -9 + 9m + 6m2 + -1(m2 + m + 1) = 0 Reorder the terms: -9 + 9m + 6m2 + -1(1 + m + m2) = 0 -9 + 9m + 6m2 + (1 * -1 + m * -1 + m2 * -1) = 0 -9 + 9m + 6m2 + (-1 + -1m + -1m2) = 0 Reorder the terms: -9 + -1 + 9m + -1m + 6m2 + -1m2 = 0 Combine like terms: -9 + -1 = -10 -10 + 9m + -1m + 6m2 + -1m2 = 0 Combine like terms: 9m + -1m = 8m -10 + 8m + 6m2 + -1m2 = 0 Combine like terms: 6m2 + -1m2 = 5m2 -10 + 8m + 5m2 = 0 Solving -10 + 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'. -2 + 1.6m + m2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 1.6m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + 1.6m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 1.6m + m2 = 0 + 2 1.6m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 1.6m + m2 = 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 = 2 + 0.64 Reorder the terms: 0.64 + 1.6m + m2 = 2 + 0.64 Combine like terms: 2 + 0.64 = 2.64 0.64 + 1.6m + m2 = 2.64 Factor a perfect square on the left side: (m + 0.8)(m + 0.8) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (m + 0.8) equal to 1.624807681 and -1.624807681.Subproblem 1
m + 0.8 = 1.624807681 Simplifying m + 0.8 = 1.624807681 Reorder the terms: 0.8 + m = 1.624807681 Solving 0.8 + m = 1.624807681 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 = 1.624807681 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + m = 1.624807681 + -0.8 m = 1.624807681 + -0.8 Combine like terms: 1.624807681 + -0.8 = 0.824807681 m = 0.824807681 Simplifying m = 0.824807681Subproblem 2
m + 0.8 = -1.624807681 Simplifying m + 0.8 = -1.624807681 Reorder the terms: 0.8 + m = -1.624807681 Solving 0.8 + m = -1.624807681 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 = -1.624807681 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + m = -1.624807681 + -0.8 m = -1.624807681 + -0.8 Combine like terms: -1.624807681 + -0.8 = -2.424807681 m = -2.424807681 Simplifying m = -2.424807681Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.824807681, -2.424807681}
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