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Simplifying 9m2 + -18m + 4 = 0 Reorder the terms: 4 + -18m + 9m2 = 0 Solving 4 + -18m + 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'. 0.4444444444 + -2m + m2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -2m + -0.4444444444 + m2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -2m + m2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -2m + m2 = 0 + -0.4444444444 -2m + m2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -2m + m2 = -0.4444444444 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = -0.4444444444 + 1 Reorder the terms: 1 + -2m + m2 = -0.4444444444 + 1 Combine like terms: -0.4444444444 + 1 = 0.5555555556 1 + -2m + m2 = 0.5555555556 Factor a perfect square on the left side: (m + -1)(m + -1) = 0.5555555556 Calculate the square root of the right side: 0.745355993 Break this problem into two subproblems by setting (m + -1) equal to 0.745355993 and -0.745355993.Subproblem 1
m + -1 = 0.745355993 Simplifying m + -1 = 0.745355993 Reorder the terms: -1 + m = 0.745355993 Solving -1 + m = 0.745355993 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 0.745355993 + 1 Combine like terms: -1 + 1 = 0 0 + m = 0.745355993 + 1 m = 0.745355993 + 1 Combine like terms: 0.745355993 + 1 = 1.745355993 m = 1.745355993 Simplifying m = 1.745355993Subproblem 2
m + -1 = -0.745355993 Simplifying m + -1 = -0.745355993 Reorder the terms: -1 + m = -0.745355993 Solving -1 + m = -0.745355993 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -0.745355993 + 1 Combine like terms: -1 + 1 = 0 0 + m = -0.745355993 + 1 m = -0.745355993 + 1 Combine like terms: -0.745355993 + 1 = 0.254644007 m = 0.254644007 Simplifying m = 0.254644007Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.745355993, 0.254644007}
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