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Simplifying 12m2 + -21 = 5m Reorder the terms: -21 + 12m2 = 5m Solving -21 + 12m2 = 5m Solving for variable 'm'. Reorder the terms: -21 + -5m + 12m2 = 5m + -5m Combine like terms: 5m + -5m = 0 -21 + -5m + 12m2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.75 + -0.4166666667m + m2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.4166666667m + 1.75 + m2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.4166666667m + m2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.4166666667m + m2 = 0 + 1.75 -0.4166666667m + m2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -0.4166666667m + m2 = 1.75 The m term is -0.4166666667m. Take half its coefficient (-0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. -0.4166666667m + 0.04340277781 + m2 = 1.75 + 0.04340277781 Reorder the terms: 0.04340277781 + -0.4166666667m + m2 = 1.75 + 0.04340277781 Combine like terms: 1.75 + 0.04340277781 = 1.79340277781 0.04340277781 + -0.4166666667m + m2 = 1.79340277781 Factor a perfect square on the left side: (m + -0.2083333334)(m + -0.2083333334) = 1.79340277781 Calculate the square root of the right side: 1.33917989 Break this problem into two subproblems by setting (m + -0.2083333334) equal to 1.33917989 and -1.33917989.Subproblem 1
m + -0.2083333334 = 1.33917989 Simplifying m + -0.2083333334 = 1.33917989 Reorder the terms: -0.2083333334 + m = 1.33917989 Solving -0.2083333334 + m = 1.33917989 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + m = 1.33917989 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + m = 1.33917989 + 0.2083333334 m = 1.33917989 + 0.2083333334 Combine like terms: 1.33917989 + 0.2083333334 = 1.5475132234 m = 1.5475132234 Simplifying m = 1.5475132234Subproblem 2
m + -0.2083333334 = -1.33917989 Simplifying m + -0.2083333334 = -1.33917989 Reorder the terms: -0.2083333334 + m = -1.33917989 Solving -0.2083333334 + m = -1.33917989 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2083333334' to each side of the equation. -0.2083333334 + 0.2083333334 + m = -1.33917989 + 0.2083333334 Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000 0.0000000000 + m = -1.33917989 + 0.2083333334 m = -1.33917989 + 0.2083333334 Combine like terms: -1.33917989 + 0.2083333334 = -1.1308465566 m = -1.1308465566 Simplifying m = -1.1308465566Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.5475132234, -1.1308465566}
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