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Simplifying 18m2 + -8m + -3 = 0 Reorder the terms: -3 + -8m + 18m2 = 0 Solving -3 + -8m + 18m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.1666666667 + -0.4444444444m + m2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.4444444444m + 0.1666666667 + m2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.4444444444m + m2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.4444444444m + m2 = 0 + 0.1666666667 -0.4444444444m + m2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.4444444444m + m2 = 0.1666666667 The m term is -0.4444444444m. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444m + 0.04938271604 + m2 = 0.1666666667 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444m + m2 = 0.1666666667 + 0.04938271604 Combine like terms: 0.1666666667 + 0.04938271604 = 0.21604938274 0.04938271604 + -0.4444444444m + m2 = 0.21604938274 Factor a perfect square on the left side: (m + -0.2222222222)(m + -0.2222222222) = 0.21604938274 Calculate the square root of the right side: 0.464811126 Break this problem into two subproblems by setting (m + -0.2222222222) equal to 0.464811126 and -0.464811126.Subproblem 1
m + -0.2222222222 = 0.464811126 Simplifying m + -0.2222222222 = 0.464811126 Reorder the terms: -0.2222222222 + m = 0.464811126 Solving -0.2222222222 + m = 0.464811126 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + m = 0.464811126 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + m = 0.464811126 + 0.2222222222 m = 0.464811126 + 0.2222222222 Combine like terms: 0.464811126 + 0.2222222222 = 0.6870333482 m = 0.6870333482 Simplifying m = 0.6870333482Subproblem 2
m + -0.2222222222 = -0.464811126 Simplifying m + -0.2222222222 = -0.464811126 Reorder the terms: -0.2222222222 + m = -0.464811126 Solving -0.2222222222 + m = -0.464811126 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + m = -0.464811126 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + m = -0.464811126 + 0.2222222222 m = -0.464811126 + 0.2222222222 Combine like terms: -0.464811126 + 0.2222222222 = -0.2425889038 m = -0.2425889038 Simplifying m = -0.2425889038Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.6870333482, -0.2425889038}
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