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Simplifying 6m2 + -13m + -1 = 0 Reorder the terms: -1 + -13m + 6m2 = 0 Solving -1 + -13m + 6m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.1666666667 + -2.166666667m + m2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -2.166666667m + 0.1666666667 + m2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -2.166666667m + m2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -2.166666667m + m2 = 0 + 0.1666666667 -2.166666667m + m2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -2.166666667m + m2 = 0.1666666667 The m term is -2.166666667m. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667m + 1.173611113 + m2 = 0.1666666667 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667m + m2 = 0.1666666667 + 1.173611113 Combine like terms: 0.1666666667 + 1.173611113 = 1.3402777797 1.173611113 + -2.166666667m + m2 = 1.3402777797 Factor a perfect square on the left side: (m + -1.083333334)(m + -1.083333334) = 1.3402777797 Calculate the square root of the right side: 1.157703667 Break this problem into two subproblems by setting (m + -1.083333334) equal to 1.157703667 and -1.157703667.Subproblem 1
m + -1.083333334 = 1.157703667 Simplifying m + -1.083333334 = 1.157703667 Reorder the terms: -1.083333334 + m = 1.157703667 Solving -1.083333334 + m = 1.157703667 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + m = 1.157703667 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + m = 1.157703667 + 1.083333334 m = 1.157703667 + 1.083333334 Combine like terms: 1.157703667 + 1.083333334 = 2.241037001 m = 2.241037001 Simplifying m = 2.241037001Subproblem 2
m + -1.083333334 = -1.157703667 Simplifying m + -1.083333334 = -1.157703667 Reorder the terms: -1.083333334 + m = -1.157703667 Solving -1.083333334 + m = -1.157703667 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + m = -1.157703667 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + m = -1.157703667 + 1.083333334 m = -1.157703667 + 1.083333334 Combine like terms: -1.157703667 + 1.083333334 = -0.074370333 m = -0.074370333 Simplifying m = -0.074370333Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.241037001, -0.074370333}
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