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Simplifying 3m2 + 17m + 21 = 0 Reorder the terms: 21 + 17m + 3m2 = 0 Solving 21 + 17m + 3m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7 + 5.666666667m + m2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 5.666666667m + -7 + m2 = 0 + -7 Reorder the terms: 7 + -7 + 5.666666667m + m2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5.666666667m + m2 = 0 + -7 5.666666667m + m2 = 0 + -7 Combine like terms: 0 + -7 = -7 5.666666667m + m2 = -7 The m term is 5.666666667m. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667m + 8.027777782 + m2 = -7 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667m + m2 = -7 + 8.027777782 Combine like terms: -7 + 8.027777782 = 1.027777782 8.027777782 + 5.666666667m + m2 = 1.027777782 Factor a perfect square on the left side: (m + 2.833333334)(m + 2.833333334) = 1.027777782 Calculate the square root of the right side: 1.013793757 Break this problem into two subproblems by setting (m + 2.833333334) equal to 1.013793757 and -1.013793757.Subproblem 1
m + 2.833333334 = 1.013793757 Simplifying m + 2.833333334 = 1.013793757 Reorder the terms: 2.833333334 + m = 1.013793757 Solving 2.833333334 + m = 1.013793757 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + m = 1.013793757 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + m = 1.013793757 + -2.833333334 m = 1.013793757 + -2.833333334 Combine like terms: 1.013793757 + -2.833333334 = -1.819539577 m = -1.819539577 Simplifying m = -1.819539577Subproblem 2
m + 2.833333334 = -1.013793757 Simplifying m + 2.833333334 = -1.013793757 Reorder the terms: 2.833333334 + m = -1.013793757 Solving 2.833333334 + m = -1.013793757 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + m = -1.013793757 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + m = -1.013793757 + -2.833333334 m = -1.013793757 + -2.833333334 Combine like terms: -1.013793757 + -2.833333334 = -3.847127091 m = -3.847127091 Simplifying m = -3.847127091Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.819539577, -3.847127091}
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