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Simplifying (3x2 + x)(9) + -1(9x + -8)(6x + 1) = 0 Reorder the terms: (x + 3x2)(9) + -1(9x + -8)(6x + 1) = 0 Reorder the terms for easier multiplication: 9(x + 3x2) + -1(9x + -8)(6x + 1) = 0 (x * 9 + 3x2 * 9) + -1(9x + -8)(6x + 1) = 0 (9x + 27x2) + -1(9x + -8)(6x + 1) = 0 Reorder the terms: 9x + 27x2 + -1(-8 + 9x)(6x + 1) = 0 Reorder the terms: 9x + 27x2 + -1(-8 + 9x)(1 + 6x) = 0 Multiply (-8 + 9x) * (1 + 6x) 9x + 27x2 + -1(-8(1 + 6x) + 9x * (1 + 6x)) = 0 9x + 27x2 + -1((1 * -8 + 6x * -8) + 9x * (1 + 6x)) = 0 9x + 27x2 + -1((-8 + -48x) + 9x * (1 + 6x)) = 0 9x + 27x2 + -1(-8 + -48x + (1 * 9x + 6x * 9x)) = 0 9x + 27x2 + -1(-8 + -48x + (9x + 54x2)) = 0 Combine like terms: -48x + 9x = -39x 9x + 27x2 + -1(-8 + -39x + 54x2) = 0 9x + 27x2 + (-8 * -1 + -39x * -1 + 54x2 * -1) = 0 9x + 27x2 + (8 + 39x + -54x2) = 0 Reorder the terms: 8 + 9x + 39x + 27x2 + -54x2 = 0 Combine like terms: 9x + 39x = 48x 8 + 48x + 27x2 + -54x2 = 0 Combine like terms: 27x2 + -54x2 = -27x2 8 + 48x + -27x2 = 0 Solving 8 + 48x + -27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -27 the coefficient of the squared term: Divide each side by '-27'. -0.2962962963 + -1.777777778x + x2 = 0 Move the constant term to the right: Add '0.2962962963' to each side of the equation. -0.2962962963 + -1.777777778x + 0.2962962963 + x2 = 0 + 0.2962962963 Reorder the terms: -0.2962962963 + 0.2962962963 + -1.777777778x + x2 = 0 + 0.2962962963 Combine like terms: -0.2962962963 + 0.2962962963 = 0.0000000000 0.0000000000 + -1.777777778x + x2 = 0 + 0.2962962963 -1.777777778x + x2 = 0 + 0.2962962963 Combine like terms: 0 + 0.2962962963 = 0.2962962963 -1.777777778x + x2 = 0.2962962963 The x term is -1.777777778x. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778x + 0.7901234570 + x2 = 0.2962962963 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778x + x2 = 0.2962962963 + 0.7901234570 Combine like terms: 0.2962962963 + 0.7901234570 = 1.0864197533 0.7901234570 + -1.777777778x + x2 = 1.0864197533 Factor a perfect square on the left side: (x + -0.888888889)(x + -0.888888889) = 1.0864197533 Calculate the square root of the right side: 1.042314613 Break this problem into two subproblems by setting (x + -0.888888889) equal to 1.042314613 and -1.042314613.Subproblem 1
x + -0.888888889 = 1.042314613 Simplifying x + -0.888888889 = 1.042314613 Reorder the terms: -0.888888889 + x = 1.042314613 Solving -0.888888889 + x = 1.042314613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = 1.042314613 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = 1.042314613 + 0.888888889 x = 1.042314613 + 0.888888889 Combine like terms: 1.042314613 + 0.888888889 = 1.931203502 x = 1.931203502 Simplifying x = 1.931203502Subproblem 2
x + -0.888888889 = -1.042314613 Simplifying x + -0.888888889 = -1.042314613 Reorder the terms: -0.888888889 + x = -1.042314613 Solving -0.888888889 + x = -1.042314613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + x = -1.042314613 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + x = -1.042314613 + 0.888888889 x = -1.042314613 + 0.888888889 Combine like terms: -1.042314613 + 0.888888889 = -0.153425724 x = -0.153425724 Simplifying x = -0.153425724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.931203502, -0.153425724}
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