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Simplifying 14m2 + 13m + -3 = 0 Reorder the terms: -3 + 13m + 14m2 = 0 Solving -3 + 13m + 14m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.2142857143 + 0.9285714286m + m2 = 0 Move the constant term to the right: Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.9285714286m + 0.2142857143 + m2 = 0 + 0.2142857143 Reorder the terms: -0.2142857143 + 0.2142857143 + 0.9285714286m + m2 = 0 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + 0.9285714286m + m2 = 0 + 0.2142857143 0.9285714286m + m2 = 0 + 0.2142857143 Combine like terms: 0 + 0.2142857143 = 0.2142857143 0.9285714286m + m2 = 0.2142857143 The m term is 0.9285714286m. Take half its coefficient (0.4642857143). Square it (0.2155612245) and add it to both sides. Add '0.2155612245' to each side of the equation. 0.9285714286m + 0.2155612245 + m2 = 0.2142857143 + 0.2155612245 Reorder the terms: 0.2155612245 + 0.9285714286m + m2 = 0.2142857143 + 0.2155612245 Combine like terms: 0.2142857143 + 0.2155612245 = 0.4298469388 0.2155612245 + 0.9285714286m + m2 = 0.4298469388 Factor a perfect square on the left side: (m + 0.4642857143)(m + 0.4642857143) = 0.4298469388 Calculate the square root of the right side: 0.655627134 Break this problem into two subproblems by setting (m + 0.4642857143) equal to 0.655627134 and -0.655627134.Subproblem 1
m + 0.4642857143 = 0.655627134 Simplifying m + 0.4642857143 = 0.655627134 Reorder the terms: 0.4642857143 + m = 0.655627134 Solving 0.4642857143 + m = 0.655627134 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + m = 0.655627134 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + m = 0.655627134 + -0.4642857143 m = 0.655627134 + -0.4642857143 Combine like terms: 0.655627134 + -0.4642857143 = 0.1913414197 m = 0.1913414197 Simplifying m = 0.1913414197Subproblem 2
m + 0.4642857143 = -0.655627134 Simplifying m + 0.4642857143 = -0.655627134 Reorder the terms: 0.4642857143 + m = -0.655627134 Solving 0.4642857143 + m = -0.655627134 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + m = -0.655627134 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + m = -0.655627134 + -0.4642857143 m = -0.655627134 + -0.4642857143 Combine like terms: -0.655627134 + -0.4642857143 = -1.1199128483 m = -1.1199128483 Simplifying m = -1.1199128483Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.1913414197, -1.1199128483}
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