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Simplifying 9m2 + 2m + -6 = 0 Reorder the terms: -6 + 2m + 9m2 = 0 Solving -6 + 2m + 9m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.6666666667 + 0.2222222222m + m2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.2222222222m + 0.6666666667 + m2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.2222222222m + m2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.2222222222m + m2 = 0 + 0.6666666667 0.2222222222m + m2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.2222222222m + m2 = 0.6666666667 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 = 0.6666666667 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222m + m2 = 0.6666666667 + 0.01234567901 Combine like terms: 0.6666666667 + 0.01234567901 = 0.67901234571 0.01234567901 + 0.2222222222m + m2 = 0.67901234571 Factor a perfect square on the left side: (m + 0.1111111111)(m + 0.1111111111) = 0.67901234571 Calculate the square root of the right side: 0.824022054 Break this problem into two subproblems by setting (m + 0.1111111111) equal to 0.824022054 and -0.824022054.Subproblem 1
m + 0.1111111111 = 0.824022054 Simplifying m + 0.1111111111 = 0.824022054 Reorder the terms: 0.1111111111 + m = 0.824022054 Solving 0.1111111111 + m = 0.824022054 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 = 0.824022054 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + m = 0.824022054 + -0.1111111111 m = 0.824022054 + -0.1111111111 Combine like terms: 0.824022054 + -0.1111111111 = 0.7129109429 m = 0.7129109429 Simplifying m = 0.7129109429Subproblem 2
m + 0.1111111111 = -0.824022054 Simplifying m + 0.1111111111 = -0.824022054 Reorder the terms: 0.1111111111 + m = -0.824022054 Solving 0.1111111111 + m = -0.824022054 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 = -0.824022054 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + m = -0.824022054 + -0.1111111111 m = -0.824022054 + -0.1111111111 Combine like terms: -0.824022054 + -0.1111111111 = -0.9351331651 m = -0.9351331651 Simplifying m = -0.9351331651Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.7129109429, -0.9351331651}
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