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Simplifying 7m2 + -12m + 1 = 0 Reorder the terms: 1 + -12m + 7m2 = 0 Solving 1 + -12m + 7m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -1.714285714m + m2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -1.714285714m + -0.1428571429 + m2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -1.714285714m + m2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -1.714285714m + m2 = 0 + -0.1428571429 -1.714285714m + m2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -1.714285714m + m2 = -0.1428571429 The m term is -1.714285714m. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714m + 0.7346938773 + m2 = -0.1428571429 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714m + m2 = -0.1428571429 + 0.7346938773 Combine like terms: -0.1428571429 + 0.7346938773 = 0.5918367344 0.7346938773 + -1.714285714m + m2 = 0.5918367344 Factor a perfect square on the left side: (m + -0.857142857)(m + -0.857142857) = 0.5918367344 Calculate the square root of the right side: 0.769309258 Break this problem into two subproblems by setting (m + -0.857142857) equal to 0.769309258 and -0.769309258.Subproblem 1
m + -0.857142857 = 0.769309258 Simplifying m + -0.857142857 = 0.769309258 Reorder the terms: -0.857142857 + m = 0.769309258 Solving -0.857142857 + m = 0.769309258 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + m = 0.769309258 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + m = 0.769309258 + 0.857142857 m = 0.769309258 + 0.857142857 Combine like terms: 0.769309258 + 0.857142857 = 1.626452115 m = 1.626452115 Simplifying m = 1.626452115Subproblem 2
m + -0.857142857 = -0.769309258 Simplifying m + -0.857142857 = -0.769309258 Reorder the terms: -0.857142857 + m = -0.769309258 Solving -0.857142857 + m = -0.769309258 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + m = -0.769309258 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + m = -0.769309258 + 0.857142857 m = -0.769309258 + 0.857142857 Combine like terms: -0.769309258 + 0.857142857 = 0.087833599 m = 0.087833599 Simplifying m = 0.087833599Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.626452115, 0.087833599}
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