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Simplifying 27x2 + 14x + -5 = 0 Reorder the terms: -5 + 14x + 27x2 = 0 Solving -5 + 14x + 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'. -0.1851851852 + 0.5185185185x + x2 = 0 Move the constant term to the right: Add '0.1851851852' to each side of the equation. -0.1851851852 + 0.5185185185x + 0.1851851852 + x2 = 0 + 0.1851851852 Reorder the terms: -0.1851851852 + 0.1851851852 + 0.5185185185x + x2 = 0 + 0.1851851852 Combine like terms: -0.1851851852 + 0.1851851852 = 0.0000000000 0.0000000000 + 0.5185185185x + x2 = 0 + 0.1851851852 0.5185185185x + x2 = 0 + 0.1851851852 Combine like terms: 0 + 0.1851851852 = 0.1851851852 0.5185185185x + x2 = 0.1851851852 The x term is 0.5185185185x. Take half its coefficient (0.2592592593). Square it (0.06721536353) and add it to both sides. Add '0.06721536353' to each side of the equation. 0.5185185185x + 0.06721536353 + x2 = 0.1851851852 + 0.06721536353 Reorder the terms: 0.06721536353 + 0.5185185185x + x2 = 0.1851851852 + 0.06721536353 Combine like terms: 0.1851851852 + 0.06721536353 = 0.25240054873 0.06721536353 + 0.5185185185x + x2 = 0.25240054873 Factor a perfect square on the left side: (x + 0.2592592593)(x + 0.2592592593) = 0.25240054873 Calculate the square root of the right side: 0.502394814 Break this problem into two subproblems by setting (x + 0.2592592593) equal to 0.502394814 and -0.502394814.Subproblem 1
x + 0.2592592593 = 0.502394814 Simplifying x + 0.2592592593 = 0.502394814 Reorder the terms: 0.2592592593 + x = 0.502394814 Solving 0.2592592593 + x = 0.502394814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2592592593' to each side of the equation. 0.2592592593 + -0.2592592593 + x = 0.502394814 + -0.2592592593 Combine like terms: 0.2592592593 + -0.2592592593 = 0.0000000000 0.0000000000 + x = 0.502394814 + -0.2592592593 x = 0.502394814 + -0.2592592593 Combine like terms: 0.502394814 + -0.2592592593 = 0.2431355547 x = 0.2431355547 Simplifying x = 0.2431355547Subproblem 2
x + 0.2592592593 = -0.502394814 Simplifying x + 0.2592592593 = -0.502394814 Reorder the terms: 0.2592592593 + x = -0.502394814 Solving 0.2592592593 + x = -0.502394814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2592592593' to each side of the equation. 0.2592592593 + -0.2592592593 + x = -0.502394814 + -0.2592592593 Combine like terms: 0.2592592593 + -0.2592592593 = 0.0000000000 0.0000000000 + x = -0.502394814 + -0.2592592593 x = -0.502394814 + -0.2592592593 Combine like terms: -0.502394814 + -0.2592592593 = -0.7616540733 x = -0.7616540733 Simplifying x = -0.7616540733Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2431355547, -0.7616540733}
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