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Simplifying 29m2 + 11m + -6 = 0 Reorder the terms: -6 + 11m + 29m2 = 0 Solving -6 + 11m + 29m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -0.2068965517 + 0.3793103448m + m2 = 0 Move the constant term to the right: Add '0.2068965517' to each side of the equation. -0.2068965517 + 0.3793103448m + 0.2068965517 + m2 = 0 + 0.2068965517 Reorder the terms: -0.2068965517 + 0.2068965517 + 0.3793103448m + m2 = 0 + 0.2068965517 Combine like terms: -0.2068965517 + 0.2068965517 = 0.0000000000 0.0000000000 + 0.3793103448m + m2 = 0 + 0.2068965517 0.3793103448m + m2 = 0 + 0.2068965517 Combine like terms: 0 + 0.2068965517 = 0.2068965517 0.3793103448m + m2 = 0.2068965517 The m term is 0.3793103448m. Take half its coefficient (0.1896551724). Square it (0.03596908442) and add it to both sides. Add '0.03596908442' to each side of the equation. 0.3793103448m + 0.03596908442 + m2 = 0.2068965517 + 0.03596908442 Reorder the terms: 0.03596908442 + 0.3793103448m + m2 = 0.2068965517 + 0.03596908442 Combine like terms: 0.2068965517 + 0.03596908442 = 0.24286563612 0.03596908442 + 0.3793103448m + m2 = 0.24286563612 Factor a perfect square on the left side: (m + 0.1896551724)(m + 0.1896551724) = 0.24286563612 Calculate the square root of the right side: 0.492813997 Break this problem into two subproblems by setting (m + 0.1896551724) equal to 0.492813997 and -0.492813997.Subproblem 1
m + 0.1896551724 = 0.492813997 Simplifying m + 0.1896551724 = 0.492813997 Reorder the terms: 0.1896551724 + m = 0.492813997 Solving 0.1896551724 + m = 0.492813997 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1896551724' to each side of the equation. 0.1896551724 + -0.1896551724 + m = 0.492813997 + -0.1896551724 Combine like terms: 0.1896551724 + -0.1896551724 = 0.0000000000 0.0000000000 + m = 0.492813997 + -0.1896551724 m = 0.492813997 + -0.1896551724 Combine like terms: 0.492813997 + -0.1896551724 = 0.3031588246 m = 0.3031588246 Simplifying m = 0.3031588246Subproblem 2
m + 0.1896551724 = -0.492813997 Simplifying m + 0.1896551724 = -0.492813997 Reorder the terms: 0.1896551724 + m = -0.492813997 Solving 0.1896551724 + m = -0.492813997 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1896551724' to each side of the equation. 0.1896551724 + -0.1896551724 + m = -0.492813997 + -0.1896551724 Combine like terms: 0.1896551724 + -0.1896551724 = 0.0000000000 0.0000000000 + m = -0.492813997 + -0.1896551724 m = -0.492813997 + -0.1896551724 Combine like terms: -0.492813997 + -0.1896551724 = -0.6824691694 m = -0.6824691694 Simplifying m = -0.6824691694Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.3031588246, -0.6824691694}
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