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Simplifying (3x + 1)(3x + 1) = 8 Reorder the terms: (1 + 3x)(3x + 1) = 8 Reorder the terms: (1 + 3x)(1 + 3x) = 8 Multiply (1 + 3x) * (1 + 3x) (1(1 + 3x) + 3x * (1 + 3x)) = 8 ((1 * 1 + 3x * 1) + 3x * (1 + 3x)) = 8 ((1 + 3x) + 3x * (1 + 3x)) = 8 (1 + 3x + (1 * 3x + 3x * 3x)) = 8 (1 + 3x + (3x + 9x2)) = 8 Combine like terms: 3x + 3x = 6x (1 + 6x + 9x2) = 8 Solving 1 + 6x + 9x2 = 8 Solving for variable 'x'. Reorder the terms: 1 + -8 + 6x + 9x2 = 8 + -8 Combine like terms: 1 + -8 = -7 -7 + 6x + 9x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -7 + 6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 0.6666666667x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 0.6666666667x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + 0.7777777778 0.6666666667x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 0.6666666667x + x2 = 0.7777777778 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 = 0.7777777778 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.7777777778 + 0.1111111112 Combine like terms: 0.7777777778 + 0.1111111112 = 0.888888889 0.1111111112 + 0.6666666667x + x2 = 0.888888889 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.888888889 Calculate the square root of the right side: 0.942809042 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.942809042 and -0.942809042.Subproblem 1
x + 0.3333333334 = 0.942809042 Simplifying x + 0.3333333334 = 0.942809042 Reorder the terms: 0.3333333334 + x = 0.942809042 Solving 0.3333333334 + x = 0.942809042 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 = 0.942809042 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.942809042 + -0.3333333334 x = 0.942809042 + -0.3333333334 Combine like terms: 0.942809042 + -0.3333333334 = 0.6094757086 x = 0.6094757086 Simplifying x = 0.6094757086Subproblem 2
x + 0.3333333334 = -0.942809042 Simplifying x + 0.3333333334 = -0.942809042 Reorder the terms: 0.3333333334 + x = -0.942809042 Solving 0.3333333334 + x = -0.942809042 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 = -0.942809042 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.942809042 + -0.3333333334 x = -0.942809042 + -0.3333333334 Combine like terms: -0.942809042 + -0.3333333334 = -1.2761423754 x = -1.2761423754 Simplifying x = -1.2761423754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6094757086, -1.2761423754}
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