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Simplifying 9m2 + 4 = 6 + m Reorder the terms: 4 + 9m2 = 6 + m Solving 4 + 9m2 = 6 + m Solving for variable 'm'. Reorder the terms: 4 + -6 + -1m + 9m2 = 6 + m + -6 + -1m Combine like terms: 4 + -6 = -2 -2 + -1m + 9m2 = 6 + m + -6 + -1m Reorder the terms: -2 + -1m + 9m2 = 6 + -6 + m + -1m Combine like terms: 6 + -6 = 0 -2 + -1m + 9m2 = 0 + m + -1m -2 + -1m + 9m2 = m + -1m Combine like terms: m + -1m = 0 -2 + -1m + 9m2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + -0.1111111111m + m2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -0.1111111111m + 0.2222222222 + m2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -0.1111111111m + m2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -0.1111111111m + m2 = 0 + 0.2222222222 -0.1111111111m + m2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -0.1111111111m + m2 = 0.2222222222 The m term is -0.1111111111m. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111m + 0.003086419752 + m2 = 0.2222222222 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111m + m2 = 0.2222222222 + 0.003086419752 Combine like terms: 0.2222222222 + 0.003086419752 = 0.225308641952 0.003086419752 + -0.1111111111m + m2 = 0.225308641952 Factor a perfect square on the left side: (m + -0.05555555555)(m + -0.05555555555) = 0.225308641952 Calculate the square root of the right side: 0.474666875 Break this problem into two subproblems by setting (m + -0.05555555555) equal to 0.474666875 and -0.474666875.Subproblem 1
m + -0.05555555555 = 0.474666875 Simplifying m + -0.05555555555 = 0.474666875 Reorder the terms: -0.05555555555 + m = 0.474666875 Solving -0.05555555555 + m = 0.474666875 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + m = 0.474666875 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + m = 0.474666875 + 0.05555555555 m = 0.474666875 + 0.05555555555 Combine like terms: 0.474666875 + 0.05555555555 = 0.53022243055 m = 0.53022243055 Simplifying m = 0.53022243055Subproblem 2
m + -0.05555555555 = -0.474666875 Simplifying m + -0.05555555555 = -0.474666875 Reorder the terms: -0.05555555555 + m = -0.474666875 Solving -0.05555555555 + m = -0.474666875 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + m = -0.474666875 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + m = -0.474666875 + 0.05555555555 m = -0.474666875 + 0.05555555555 Combine like terms: -0.474666875 + 0.05555555555 = -0.41911131945 m = -0.41911131945 Simplifying m = -0.41911131945Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.53022243055, -0.41911131945}
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