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Simplifying 27m2 + 2m + -9 = 0 Reorder the terms: -9 + 2m + 27m2 = 0 Solving -9 + 2m + 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'. -0.3333333333 + 0.07407407407m + m2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.07407407407m + 0.3333333333 + m2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.07407407407m + m2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.07407407407m + m2 = 0 + 0.3333333333 0.07407407407m + m2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.07407407407m + m2 = 0.3333333333 The m term is 0.07407407407m. Take half its coefficient (0.03703703704). Square it (0.001371742113) and add it to both sides. Add '0.001371742113' to each side of the equation. 0.07407407407m + 0.001371742113 + m2 = 0.3333333333 + 0.001371742113 Reorder the terms: 0.001371742113 + 0.07407407407m + m2 = 0.3333333333 + 0.001371742113 Combine like terms: 0.3333333333 + 0.001371742113 = 0.334705075413 0.001371742113 + 0.07407407407m + m2 = 0.334705075413 Factor a perfect square on the left side: (m + 0.03703703704)(m + 0.03703703704) = 0.334705075413 Calculate the square root of the right side: 0.578537013 Break this problem into two subproblems by setting (m + 0.03703703704) equal to 0.578537013 and -0.578537013.Subproblem 1
m + 0.03703703704 = 0.578537013 Simplifying m + 0.03703703704 = 0.578537013 Reorder the terms: 0.03703703704 + m = 0.578537013 Solving 0.03703703704 + m = 0.578537013 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.03703703704' to each side of the equation. 0.03703703704 + -0.03703703704 + m = 0.578537013 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + m = 0.578537013 + -0.03703703704 m = 0.578537013 + -0.03703703704 Combine like terms: 0.578537013 + -0.03703703704 = 0.54149997596 m = 0.54149997596 Simplifying m = 0.54149997596Subproblem 2
m + 0.03703703704 = -0.578537013 Simplifying m + 0.03703703704 = -0.578537013 Reorder the terms: 0.03703703704 + m = -0.578537013 Solving 0.03703703704 + m = -0.578537013 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.03703703704' to each side of the equation. 0.03703703704 + -0.03703703704 + m = -0.578537013 + -0.03703703704 Combine like terms: 0.03703703704 + -0.03703703704 = 0.00000000000 0.00000000000 + m = -0.578537013 + -0.03703703704 m = -0.578537013 + -0.03703703704 Combine like terms: -0.578537013 + -0.03703703704 = -0.61557405004 m = -0.61557405004 Simplifying m = -0.61557405004Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.54149997596, -0.61557405004}
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