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Simplifying 9x(x + 6) + -1(3x + 1) = 1 Reorder the terms: 9x(6 + x) + -1(3x + 1) = 1 (6 * 9x + x * 9x) + -1(3x + 1) = 1 (54x + 9x2) + -1(3x + 1) = 1 Reorder the terms: 54x + 9x2 + -1(1 + 3x) = 1 54x + 9x2 + (1 * -1 + 3x * -1) = 1 54x + 9x2 + (-1 + -3x) = 1 Reorder the terms: -1 + 54x + -3x + 9x2 = 1 Combine like terms: 54x + -3x = 51x -1 + 51x + 9x2 = 1 Solving -1 + 51x + 9x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -1 + 51x + 9x2 = 1 + -1 Combine like terms: -1 + -1 = -2 -2 + 51x + 9x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -2 + 51x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + 5.666666667x + x2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + 5.666666667x + 0.2222222222 + x2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + 5.666666667x + x2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + 5.666666667x + x2 = 0 + 0.2222222222 5.666666667x + x2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 5.666666667x + x2 = 0.2222222222 The x term is 5.666666667x. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667x + 8.027777782 + x2 = 0.2222222222 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667x + x2 = 0.2222222222 + 8.027777782 Combine like terms: 0.2222222222 + 8.027777782 = 8.2500000042 8.027777782 + 5.666666667x + x2 = 8.2500000042 Factor a perfect square on the left side: (x + 2.833333334)(x + 2.833333334) = 8.2500000042 Calculate the square root of the right side: 2.872281324 Break this problem into two subproblems by setting (x + 2.833333334) equal to 2.872281324 and -2.872281324.Subproblem 1
x + 2.833333334 = 2.872281324 Simplifying x + 2.833333334 = 2.872281324 Reorder the terms: 2.833333334 + x = 2.872281324 Solving 2.833333334 + x = 2.872281324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = 2.872281324 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = 2.872281324 + -2.833333334 x = 2.872281324 + -2.833333334 Combine like terms: 2.872281324 + -2.833333334 = 0.03894799 x = 0.03894799 Simplifying x = 0.03894799Subproblem 2
x + 2.833333334 = -2.872281324 Simplifying x + 2.833333334 = -2.872281324 Reorder the terms: 2.833333334 + x = -2.872281324 Solving 2.833333334 + x = -2.872281324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + x = -2.872281324 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + x = -2.872281324 + -2.833333334 x = -2.872281324 + -2.833333334 Combine like terms: -2.872281324 + -2.833333334 = -5.705614658 x = -5.705614658 Simplifying x = -5.705614658Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.03894799, -5.705614658}
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