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Simplifying 9m2 + -7m + -70 = 0 Reorder the terms: -70 + -7m + 9m2 = 0 Solving -70 + -7m + 9m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -7.777777778 + -0.7777777778m + m2 = 0 Move the constant term to the right: Add '7.777777778' to each side of the equation. -7.777777778 + -0.7777777778m + 7.777777778 + m2 = 0 + 7.777777778 Reorder the terms: -7.777777778 + 7.777777778 + -0.7777777778m + m2 = 0 + 7.777777778 Combine like terms: -7.777777778 + 7.777777778 = 0.000000000 0.000000000 + -0.7777777778m + m2 = 0 + 7.777777778 -0.7777777778m + m2 = 0 + 7.777777778 Combine like terms: 0 + 7.777777778 = 7.777777778 -0.7777777778m + m2 = 7.777777778 The m term is -0.7777777778m. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778m + 0.1512345679 + m2 = 7.777777778 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778m + m2 = 7.777777778 + 0.1512345679 Combine like terms: 7.777777778 + 0.1512345679 = 7.9290123459 0.1512345679 + -0.7777777778m + m2 = 7.9290123459 Factor a perfect square on the left side: (m + -0.3888888889)(m + -0.3888888889) = 7.9290123459 Calculate the square root of the right side: 2.815850199 Break this problem into two subproblems by setting (m + -0.3888888889) equal to 2.815850199 and -2.815850199.Subproblem 1
m + -0.3888888889 = 2.815850199 Simplifying m + -0.3888888889 = 2.815850199 Reorder the terms: -0.3888888889 + m = 2.815850199 Solving -0.3888888889 + m = 2.815850199 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + m = 2.815850199 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + m = 2.815850199 + 0.3888888889 m = 2.815850199 + 0.3888888889 Combine like terms: 2.815850199 + 0.3888888889 = 3.2047390879 m = 3.2047390879 Simplifying m = 3.2047390879Subproblem 2
m + -0.3888888889 = -2.815850199 Simplifying m + -0.3888888889 = -2.815850199 Reorder the terms: -0.3888888889 + m = -2.815850199 Solving -0.3888888889 + m = -2.815850199 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + m = -2.815850199 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + m = -2.815850199 + 0.3888888889 m = -2.815850199 + 0.3888888889 Combine like terms: -2.815850199 + 0.3888888889 = -2.4269613101 m = -2.4269613101 Simplifying m = -2.4269613101Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.2047390879, -2.4269613101}
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