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Simplifying 27x2 + 12x + -1 = 0 Reorder the terms: -1 + 12x + 27x2 = 0 Solving -1 + 12x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.03703703704 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '0.03703703704' to each side of the equation. -0.03703703704 + 0.4444444444x + 0.03703703704 + x2 = 0 + 0.03703703704 Reorder the terms: -0.03703703704 + 0.03703703704 + 0.4444444444x + x2 = 0 + 0.03703703704 Combine like terms: -0.03703703704 + 0.03703703704 = 0.00000000000 0.00000000000 + 0.4444444444x + x2 = 0 + 0.03703703704 0.4444444444x + x2 = 0 + 0.03703703704 Combine like terms: 0 + 0.03703703704 = 0.03703703704 0.4444444444x + x2 = 0.03703703704 The x term is 0.4444444444x. 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. 0.4444444444x + 0.04938271604 + x2 = 0.03703703704 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 0.03703703704 + 0.04938271604 Combine like terms: 0.03703703704 + 0.04938271604 = 0.08641975308 0.04938271604 + 0.4444444444x + x2 = 0.08641975308 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 0.08641975308 Calculate the square root of the right side: 0.293972368 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 0.293972368 and -0.293972368.Subproblem 1
x + 0.2222222222 = 0.293972368 Simplifying x + 0.2222222222 = 0.293972368 Reorder the terms: 0.2222222222 + x = 0.293972368 Solving 0.2222222222 + x = 0.293972368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 0.293972368 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 0.293972368 + -0.2222222222 x = 0.293972368 + -0.2222222222 Combine like terms: 0.293972368 + -0.2222222222 = 0.0717501458 x = 0.0717501458 Simplifying x = 0.0717501458Subproblem 2
x + 0.2222222222 = -0.293972368 Simplifying x + 0.2222222222 = -0.293972368 Reorder the terms: 0.2222222222 + x = -0.293972368 Solving 0.2222222222 + x = -0.293972368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -0.293972368 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -0.293972368 + -0.2222222222 x = -0.293972368 + -0.2222222222 Combine like terms: -0.293972368 + -0.2222222222 = -0.5161945902 x = -0.5161945902 Simplifying x = -0.5161945902Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0717501458, -0.5161945902}
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