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Simplifying 9m2 + 2m = 8 Reorder the terms: 2m + 9m2 = 8 Solving 2m + 9m2 = 8 Solving for variable 'm'. Reorder the terms: -8 + 2m + 9m2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 2m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 0.2222222222m + m2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.2222222222m + 0.8888888889 + m2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.2222222222m + m2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.2222222222m + m2 = 0 + 0.8888888889 0.2222222222m + m2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.2222222222m + m2 = 0.8888888889 The m term is 0.2222222222m. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222m + 0.01234567901 + m2 = 0.8888888889 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222m + m2 = 0.8888888889 + 0.01234567901 Combine like terms: 0.8888888889 + 0.01234567901 = 0.90123456791 0.01234567901 + 0.2222222222m + m2 = 0.90123456791 Factor a perfect square on the left side: (m + 0.1111111111)(m + 0.1111111111) = 0.90123456791 Calculate the square root of the right side: 0.949333749 Break this problem into two subproblems by setting (m + 0.1111111111) equal to 0.949333749 and -0.949333749.Subproblem 1
m + 0.1111111111 = 0.949333749 Simplifying m + 0.1111111111 = 0.949333749 Reorder the terms: 0.1111111111 + m = 0.949333749 Solving 0.1111111111 + m = 0.949333749 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + m = 0.949333749 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + m = 0.949333749 + -0.1111111111 m = 0.949333749 + -0.1111111111 Combine like terms: 0.949333749 + -0.1111111111 = 0.8382226379 m = 0.8382226379 Simplifying m = 0.8382226379Subproblem 2
m + 0.1111111111 = -0.949333749 Simplifying m + 0.1111111111 = -0.949333749 Reorder the terms: 0.1111111111 + m = -0.949333749 Solving 0.1111111111 + m = -0.949333749 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + m = -0.949333749 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + m = -0.949333749 + -0.1111111111 m = -0.949333749 + -0.1111111111 Combine like terms: -0.949333749 + -0.1111111111 = -1.0604448601 m = -1.0604448601 Simplifying m = -1.0604448601Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.8382226379, -1.0604448601}
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