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Simplifying 14m2 + 1 = 6m + 7m Reorder the terms: 1 + 14m2 = 6m + 7m Combine like terms: 6m + 7m = 13m 1 + 14m2 = 13m Solving 1 + 14m2 = 13m Solving for variable 'm'. Reorder the terms: 1 + -13m + 14m2 = 13m + -13m Combine like terms: 13m + -13m = 0 1 + -13m + 14m2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.07142857143 + -0.9285714286m + m2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + -0.9285714286m + -0.07142857143 + m2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + -0.9285714286m + m2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + -0.9285714286m + m2 = 0 + -0.07142857143 -0.9285714286m + m2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 -0.9285714286m + m2 = -0.07142857143 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 = -0.07142857143 + 0.2155612245 Reorder the terms: 0.2155612245 + -0.9285714286m + m2 = -0.07142857143 + 0.2155612245 Combine like terms: -0.07142857143 + 0.2155612245 = 0.14413265307 0.2155612245 + -0.9285714286m + m2 = 0.14413265307 Factor a perfect square on the left side: (m + -0.4642857143)(m + -0.4642857143) = 0.14413265307 Calculate the square root of the right side: 0.379648065 Break this problem into two subproblems by setting (m + -0.4642857143) equal to 0.379648065 and -0.379648065.Subproblem 1
m + -0.4642857143 = 0.379648065 Simplifying m + -0.4642857143 = 0.379648065 Reorder the terms: -0.4642857143 + m = 0.379648065 Solving -0.4642857143 + m = 0.379648065 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 = 0.379648065 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + m = 0.379648065 + 0.4642857143 m = 0.379648065 + 0.4642857143 Combine like terms: 0.379648065 + 0.4642857143 = 0.8439337793 m = 0.8439337793 Simplifying m = 0.8439337793Subproblem 2
m + -0.4642857143 = -0.379648065 Simplifying m + -0.4642857143 = -0.379648065 Reorder the terms: -0.4642857143 + m = -0.379648065 Solving -0.4642857143 + m = -0.379648065 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 = -0.379648065 + 0.4642857143 Combine like terms: -0.4642857143 + 0.4642857143 = 0.0000000000 0.0000000000 + m = -0.379648065 + 0.4642857143 m = -0.379648065 + 0.4642857143 Combine like terms: -0.379648065 + 0.4642857143 = 0.0846376493 m = 0.0846376493 Simplifying m = 0.0846376493Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.8439337793, 0.0846376493}
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