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Simplifying (3x + -1) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Reorder the terms: (-1 + 3x) + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Remove parenthesis around (-1 + 3x) -1 + 3x + -3(2x + 3)(2x + 3) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Reorder the terms: -1 + 3x + -3(3 + 2x)(2x + 3) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Reorder the terms: -1 + 3x + -3(3 + 2x)(3 + 2x) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Multiply (3 + 2x) * (3 + 2x) -1 + 3x + -3(3(3 + 2x) + 2x * (3 + 2x)) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) -1 + 3x + -3((3 * 3 + 2x * 3) + 2x * (3 + 2x)) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) -1 + 3x + -3((9 + 6x) + 2x * (3 + 2x)) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) -1 + 3x + -3(9 + 6x + (3 * 2x + 2x * 2x)) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) -1 + 3x + -3(9 + 6x + (6x + 4x2)) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Combine like terms: 6x + 6x = 12x -1 + 3x + -3(9 + 12x + 4x2) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) -1 + 3x + (9 * -3 + 12x * -3 + 4x2 * -3) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) -1 + 3x + (-27 + -36x + -12x2) + 42 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Reorder the terms: -1 + -27 + 42 + 3x + -36x + -12x2 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Combine like terms: -1 + -27 = -28 -28 + 42 + 3x + -36x + -12x2 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Combine like terms: -28 + 42 = 14 14 + 3x + -36x + -12x2 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Combine like terms: 3x + -36x = -33x 14 + -33x + -12x2 = 2x(-1x + -5) + -1(-1x + 1)(x + -1) Reorder the terms: 14 + -33x + -12x2 = 2x(-5 + -1x) + -1(-1x + 1)(x + -1) 14 + -33x + -12x2 = (-5 * 2x + -1x * 2x) + -1(-1x + 1)(x + -1) 14 + -33x + -12x2 = (-10x + -2x2) + -1(-1x + 1)(x + -1) Reorder the terms: 14 + -33x + -12x2 = -10x + -2x2 + -1(1 + -1x)(x + -1) Reorder the terms: 14 + -33x + -12x2 = -10x + -2x2 + -1(1 + -1x)(-1 + x) Multiply (1 + -1x) * (-1 + x) 14 + -33x + -12x2 = -10x + -2x2 + -1(1(-1 + x) + -1x * (-1 + x)) 14 + -33x + -12x2 = -10x + -2x2 + -1((-1 * 1 + x * 1) + -1x * (-1 + x)) 14 + -33x + -12x2 = -10x + -2x2 + -1((-1 + 1x) + -1x * (-1 + x)) 14 + -33x + -12x2 = -10x + -2x2 + -1(-1 + 1x + (-1 * -1x + x * -1x)) 14 + -33x + -12x2 = -10x + -2x2 + -1(-1 + 1x + (1x + -1x2)) Combine like terms: 1x + 1x = 2x 14 + -33x + -12x2 = -10x + -2x2 + -1(-1 + 2x + -1x2) 14 + -33x + -12x2 = -10x + -2x2 + (-1 * -1 + 2x * -1 + -1x2 * -1) 14 + -33x + -12x2 = -10x + -2x2 + (1 + -2x + 1x2) Reorder the terms: 14 + -33x + -12x2 = 1 + -10x + -2x + -2x2 + 1x2 Combine like terms: -10x + -2x = -12x 14 + -33x + -12x2 = 1 + -12x + -2x2 + 1x2 Combine like terms: -2x2 + 1x2 = -1x2 14 + -33x + -12x2 = 1 + -12x + -1x2 Solving 14 + -33x + -12x2 = 1 + -12x + -1x2 Solving for variable 'x'. Reorder the terms: 14 + -1 + -33x + 12x + -12x2 + x2 = 1 + -12x + -1x2 + -1 + 12x + x2 Combine like terms: 14 + -1 = 13 13 + -33x + 12x + -12x2 + x2 = 1 + -12x + -1x2 + -1 + 12x + x2 Combine like terms: -33x + 12x = -21x 13 + -21x + -12x2 + x2 = 1 + -12x + -1x2 + -1 + 12x + x2 Combine like terms: -12x2 + x2 = -11x2 13 + -21x + -11x2 = 1 + -12x + -1x2 + -1 + 12x + x2 Reorder the terms: 13 + -21x + -11x2 = 1 + -1 + -12x + 12x + -1x2 + x2 Combine like terms: 1 + -1 = 0 13 + -21x + -11x2 = 0 + -12x + 12x + -1x2 + x2 13 + -21x + -11x2 = -12x + 12x + -1x2 + x2 Combine like terms: -12x + 12x = 0 13 + -21x + -11x2 = 0 + -1x2 + x2 13 + -21x + -11x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 13 + -21x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -1.181818182 + 1.909090909x + x2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + 1.909090909x + 1.181818182 + x2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + 1.909090909x + x2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + 1.909090909x + x2 = 0 + 1.181818182 1.909090909x + x2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 1.909090909x + x2 = 1.181818182 The x term is 1.909090909x. Take half its coefficient (0.9545454545). Square it (0.9111570247) and add it to both sides. Add '0.9111570247' to each side of the equation. 1.909090909x + 0.9111570247 + x2 = 1.181818182 + 0.9111570247 Reorder the terms: 0.9111570247 + 1.909090909x + x2 = 1.181818182 + 0.9111570247 Combine like terms: 1.181818182 + 0.9111570247 = 2.0929752067 0.9111570247 + 1.909090909x + x2 = 2.0929752067 Factor a perfect square on the left side: (x + 0.9545454545)(x + 0.9545454545) = 2.0929752067 Calculate the square root of the right side: 1.44671186 Break this problem into two subproblems by setting (x + 0.9545454545) equal to 1.44671186 and -1.44671186.Subproblem 1
x + 0.9545454545 = 1.44671186 Simplifying x + 0.9545454545 = 1.44671186 Reorder the terms: 0.9545454545 + x = 1.44671186 Solving 0.9545454545 + x = 1.44671186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9545454545' to each side of the equation. 0.9545454545 + -0.9545454545 + x = 1.44671186 + -0.9545454545 Combine like terms: 0.9545454545 + -0.9545454545 = 0.0000000000 0.0000000000 + x = 1.44671186 + -0.9545454545 x = 1.44671186 + -0.9545454545 Combine like terms: 1.44671186 + -0.9545454545 = 0.4921664055 x = 0.4921664055 Simplifying x = 0.4921664055Subproblem 2
x + 0.9545454545 = -1.44671186 Simplifying x + 0.9545454545 = -1.44671186 Reorder the terms: 0.9545454545 + x = -1.44671186 Solving 0.9545454545 + x = -1.44671186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9545454545' to each side of the equation. 0.9545454545 + -0.9545454545 + x = -1.44671186 + -0.9545454545 Combine like terms: 0.9545454545 + -0.9545454545 = 0.0000000000 0.0000000000 + x = -1.44671186 + -0.9545454545 x = -1.44671186 + -0.9545454545 Combine like terms: -1.44671186 + -0.9545454545 = -2.4012573145 x = -2.4012573145 Simplifying x = -2.4012573145Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4921664055, -2.4012573145}
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