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Simplifying -9(3m2 + 2m) + 2 = 0 Reorder the terms: -9(2m + 3m2) + 2 = 0 (2m * -9 + 3m2 * -9) + 2 = 0 (-18m + -27m2) + 2 = 0 Reorder the terms: 2 + -18m + -27m2 = 0 Solving 2 + -18m + -27m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. -0.07407407407 + 0.6666666667m + m2 = 0 Move the constant term to the right: Add '0.07407407407' to each side of the equation. -0.07407407407 + 0.6666666667m + 0.07407407407 + m2 = 0 + 0.07407407407 Reorder the terms: -0.07407407407 + 0.07407407407 + 0.6666666667m + m2 = 0 + 0.07407407407 Combine like terms: -0.07407407407 + 0.07407407407 = 0.00000000000 0.00000000000 + 0.6666666667m + m2 = 0 + 0.07407407407 0.6666666667m + m2 = 0 + 0.07407407407 Combine like terms: 0 + 0.07407407407 = 0.07407407407 0.6666666667m + m2 = 0.07407407407 The m term is 0.6666666667m. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667m + 0.1111111112 + m2 = 0.07407407407 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667m + m2 = 0.07407407407 + 0.1111111112 Combine like terms: 0.07407407407 + 0.1111111112 = 0.18518518527 0.1111111112 + 0.6666666667m + m2 = 0.18518518527 Factor a perfect square on the left side: (m + 0.3333333334)(m + 0.3333333334) = 0.18518518527 Calculate the square root of the right side: 0.430331483 Break this problem into two subproblems by setting (m + 0.3333333334) equal to 0.430331483 and -0.430331483.Subproblem 1
m + 0.3333333334 = 0.430331483 Simplifying m + 0.3333333334 = 0.430331483 Reorder the terms: 0.3333333334 + m = 0.430331483 Solving 0.3333333334 + m = 0.430331483 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + m = 0.430331483 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + m = 0.430331483 + -0.3333333334 m = 0.430331483 + -0.3333333334 Combine like terms: 0.430331483 + -0.3333333334 = 0.0969981496 m = 0.0969981496 Simplifying m = 0.0969981496Subproblem 2
m + 0.3333333334 = -0.430331483 Simplifying m + 0.3333333334 = -0.430331483 Reorder the terms: 0.3333333334 + m = -0.430331483 Solving 0.3333333334 + m = -0.430331483 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + m = -0.430331483 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + m = -0.430331483 + -0.3333333334 m = -0.430331483 + -0.3333333334 Combine like terms: -0.430331483 + -0.3333333334 = -0.7636648164 m = -0.7636648164 Simplifying m = -0.7636648164Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.0969981496, -0.7636648164}
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