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Simplifying 3(3x + -1)(3x + -1) = 7 Reorder the terms: 3(-1 + 3x)(3x + -1) = 7 Reorder the terms: 3(-1 + 3x)(-1 + 3x) = 7 Multiply (-1 + 3x) * (-1 + 3x) 3(-1(-1 + 3x) + 3x * (-1 + 3x)) = 7 3((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 7 3((1 + -3x) + 3x * (-1 + 3x)) = 7 3(1 + -3x + (-1 * 3x + 3x * 3x)) = 7 3(1 + -3x + (-3x + 9x2)) = 7 Combine like terms: -3x + -3x = -6x 3(1 + -6x + 9x2) = 7 (1 * 3 + -6x * 3 + 9x2 * 3) = 7 (3 + -18x + 27x2) = 7 Solving 3 + -18x + 27x2 = 7 Solving for variable 'x'. Reorder the terms: 3 + -7 + -18x + 27x2 = 7 + -7 Combine like terms: 3 + -7 = -4 -4 + -18x + 27x2 = 7 + -7 Combine like terms: 7 + -7 = 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 = 0.8425084104 x = 0.8425084104 Simplifying x = 0.8425084104Subproblem 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 = -0.1758417436 x = -0.1758417436 Simplifying x = -0.1758417436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8425084104, -0.1758417436}
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