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Simplifying 27x2 + 18x = 4 Reorder the terms: 18x + 27x2 = 4 Solving 18x + 27x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 18x + 27x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 18x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.1481481481 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.1481481481' to each side of the equation. -0.1481481481 + 0.6666666667x + 0.1481481481 + x2 = 0 + 0.1481481481 Reorder the terms: -0.1481481481 + 0.1481481481 + 0.6666666667x + x2 = 0 + 0.1481481481 Combine like terms: -0.1481481481 + 0.1481481481 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + 0.1481481481 0.6666666667x + x2 = 0 + 0.1481481481 Combine like terms: 0 + 0.1481481481 = 0.1481481481 0.6666666667x + x2 = 0.1481481481 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.1481481481 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.1481481481 + 0.1111111112 Combine like terms: 0.1481481481 + 0.1111111112 = 0.2592592593 0.1111111112 + 0.6666666667x + x2 = 0.2592592593 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.2592592593 Calculate the square root of the right side: 0.509175077 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.509175077 and -0.509175077.Subproblem 1
x + 0.3333333334 = 0.509175077 Simplifying x + 0.3333333334 = 0.509175077 Reorder the terms: 0.3333333334 + x = 0.509175077 Solving 0.3333333334 + x = 0.509175077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.509175077 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.509175077 + -0.3333333334 x = 0.509175077 + -0.3333333334 Combine like terms: 0.509175077 + -0.3333333334 = 0.1758417436 x = 0.1758417436 Simplifying x = 0.1758417436Subproblem 2
x + 0.3333333334 = -0.509175077 Simplifying x + 0.3333333334 = -0.509175077 Reorder the terms: 0.3333333334 + x = -0.509175077 Solving 0.3333333334 + x = -0.509175077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.509175077 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.509175077 + -0.3333333334 x = -0.509175077 + -0.3333333334 Combine like terms: -0.509175077 + -0.3333333334 = -0.8425084104 x = -0.8425084104 Simplifying x = -0.8425084104Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1758417436, -0.8425084104}
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