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Simplifying 2(1 + -7m) + 1 = -3m(1 + -12m) (1 * 2 + -7m * 2) + 1 = -3m(1 + -12m) (2 + -14m) + 1 = -3m(1 + -12m) Reorder the terms: 2 + 1 + -14m = -3m(1 + -12m) Combine like terms: 2 + 1 = 3 3 + -14m = -3m(1 + -12m) 3 + -14m = (1 * -3m + -12m * -3m) 3 + -14m = (-3m + 36m2) Solving 3 + -14m = -3m + 36m2 Solving for variable 'm'. Combine like terms: -14m + 3m = -11m 3 + -11m + -36m2 = -3m + 36m2 + 3m + -36m2 Reorder the terms: 3 + -11m + -36m2 = -3m + 3m + 36m2 + -36m2 Combine like terms: -3m + 3m = 0 3 + -11m + -36m2 = 0 + 36m2 + -36m2 3 + -11m + -36m2 = 36m2 + -36m2 Combine like terms: 36m2 + -36m2 = 0 3 + -11m + -36m2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -0.08333333333 + 0.3055555556m + m2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.3055555556m + 0.08333333333 + m2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.3055555556m + m2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.3055555556m + m2 = 0 + 0.08333333333 0.3055555556m + m2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.3055555556m + m2 = 0.08333333333 The m term is 0.3055555556m. Take half its coefficient (0.1527777778). Square it (0.02334104939) and add it to both sides. Add '0.02334104939' to each side of the equation. 0.3055555556m + 0.02334104939 + m2 = 0.08333333333 + 0.02334104939 Reorder the terms: 0.02334104939 + 0.3055555556m + m2 = 0.08333333333 + 0.02334104939 Combine like terms: 0.08333333333 + 0.02334104939 = 0.10667438272 0.02334104939 + 0.3055555556m + m2 = 0.10667438272 Factor a perfect square on the left side: (m + 0.1527777778)(m + 0.1527777778) = 0.10667438272 Calculate the square root of the right side: 0.326610445 Break this problem into two subproblems by setting (m + 0.1527777778) equal to 0.326610445 and -0.326610445.Subproblem 1
m + 0.1527777778 = 0.326610445 Simplifying m + 0.1527777778 = 0.326610445 Reorder the terms: 0.1527777778 + m = 0.326610445 Solving 0.1527777778 + m = 0.326610445 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1527777778' to each side of the equation. 0.1527777778 + -0.1527777778 + m = 0.326610445 + -0.1527777778 Combine like terms: 0.1527777778 + -0.1527777778 = 0.0000000000 0.0000000000 + m = 0.326610445 + -0.1527777778 m = 0.326610445 + -0.1527777778 Combine like terms: 0.326610445 + -0.1527777778 = 0.1738326672 m = 0.1738326672 Simplifying m = 0.1738326672Subproblem 2
m + 0.1527777778 = -0.326610445 Simplifying m + 0.1527777778 = -0.326610445 Reorder the terms: 0.1527777778 + m = -0.326610445 Solving 0.1527777778 + m = -0.326610445 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.1527777778' to each side of the equation. 0.1527777778 + -0.1527777778 + m = -0.326610445 + -0.1527777778 Combine like terms: 0.1527777778 + -0.1527777778 = 0.0000000000 0.0000000000 + m = -0.326610445 + -0.1527777778 m = -0.326610445 + -0.1527777778 Combine like terms: -0.326610445 + -0.1527777778 = -0.4793882228 m = -0.4793882228 Simplifying m = -0.4793882228Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.1738326672, -0.4793882228}
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