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Simplifying (3x + -1)(3x + -1) = 75 Reorder the terms: (-1 + 3x)(3x + -1) = 75 Reorder the terms: (-1 + 3x)(-1 + 3x) = 75 Multiply (-1 + 3x) * (-1 + 3x) (-1(-1 + 3x) + 3x * (-1 + 3x)) = 75 ((-1 * -1 + 3x * -1) + 3x * (-1 + 3x)) = 75 ((1 + -3x) + 3x * (-1 + 3x)) = 75 (1 + -3x + (-1 * 3x + 3x * 3x)) = 75 (1 + -3x + (-3x + 9x2)) = 75 Combine like terms: -3x + -3x = -6x (1 + -6x + 9x2) = 75 Solving 1 + -6x + 9x2 = 75 Solving for variable 'x'. Reorder the terms: 1 + -75 + -6x + 9x2 = 75 + -75 Combine like terms: 1 + -75 = -74 -74 + -6x + 9x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -74 + -6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8.222222222 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '8.222222222' to each side of the equation. -8.222222222 + -0.6666666667x + 8.222222222 + x2 = 0 + 8.222222222 Reorder the terms: -8.222222222 + 8.222222222 + -0.6666666667x + x2 = 0 + 8.222222222 Combine like terms: -8.222222222 + 8.222222222 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + 8.222222222 -0.6666666667x + x2 = 0 + 8.222222222 Combine like terms: 0 + 8.222222222 = 8.222222222 -0.6666666667x + x2 = 8.222222222 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 = 8.222222222 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = 8.222222222 + 0.1111111112 Combine like terms: 8.222222222 + 0.1111111112 = 8.3333333332 0.1111111112 + -0.6666666667x + x2 = 8.3333333332 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = 8.3333333332 Calculate the square root of the right side: 2.886751346 Break this problem into two subproblems by setting (x + -0.3333333334) equal to 2.886751346 and -2.886751346.Subproblem 1
x + -0.3333333334 = 2.886751346 Simplifying x + -0.3333333334 = 2.886751346 Reorder the terms: -0.3333333334 + x = 2.886751346 Solving -0.3333333334 + x = 2.886751346 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 = 2.886751346 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = 2.886751346 + 0.3333333334 x = 2.886751346 + 0.3333333334 Combine like terms: 2.886751346 + 0.3333333334 = 3.2200846794 x = 3.2200846794 Simplifying x = 3.2200846794Subproblem 2
x + -0.3333333334 = -2.886751346 Simplifying x + -0.3333333334 = -2.886751346 Reorder the terms: -0.3333333334 + x = -2.886751346 Solving -0.3333333334 + x = -2.886751346 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 = -2.886751346 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + x = -2.886751346 + 0.3333333334 x = -2.886751346 + 0.3333333334 Combine like terms: -2.886751346 + 0.3333333334 = -2.5534180126 x = -2.5534180126 Simplifying x = -2.5534180126Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.2200846794, -2.5534180126}
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