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Simplifying 9m2 + -14m + -16 = 0 Reorder the terms: -16 + -14m + 9m2 = 0 Solving -16 + -14m + 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'. -1.777777778 + -1.555555556m + m2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -1.555555556m + 1.777777778 + m2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -1.555555556m + m2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -1.555555556m + m2 = 0 + 1.777777778 -1.555555556m + m2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -1.555555556m + m2 = 1.777777778 The m term is -1.555555556m. Take half its coefficient (-0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. -1.555555556m + 0.6049382720 + m2 = 1.777777778 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556m + m2 = 1.777777778 + 0.6049382720 Combine like terms: 1.777777778 + 0.6049382720 = 2.38271605 0.6049382720 + -1.555555556m + m2 = 2.38271605 Factor a perfect square on the left side: (m + -0.777777778)(m + -0.777777778) = 2.38271605 Calculate the square root of the right side: 1.543604888 Break this problem into two subproblems by setting (m + -0.777777778) equal to 1.543604888 and -1.543604888.Subproblem 1
m + -0.777777778 = 1.543604888 Simplifying m + -0.777777778 = 1.543604888 Reorder the terms: -0.777777778 + m = 1.543604888 Solving -0.777777778 + m = 1.543604888 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + m = 1.543604888 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + m = 1.543604888 + 0.777777778 m = 1.543604888 + 0.777777778 Combine like terms: 1.543604888 + 0.777777778 = 2.321382666 m = 2.321382666 Simplifying m = 2.321382666Subproblem 2
m + -0.777777778 = -1.543604888 Simplifying m + -0.777777778 = -1.543604888 Reorder the terms: -0.777777778 + m = -1.543604888 Solving -0.777777778 + m = -1.543604888 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + m = -1.543604888 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + m = -1.543604888 + 0.777777778 m = -1.543604888 + 0.777777778 Combine like terms: -1.543604888 + 0.777777778 = -0.76582711 m = -0.76582711 Simplifying m = -0.76582711Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.321382666, -0.76582711}
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