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Simplifying 5x + 4 + -3(2x + -1) = 8 + -1(7x + -1) * x Reorder the terms: 5x + 4 + -3(-1 + 2x) = 8 + -1(7x + -1) * x 5x + 4 + (-1 * -3 + 2x * -3) = 8 + -1(7x + -1) * x 5x + 4 + (3 + -6x) = 8 + -1(7x + -1) * x Reorder the terms: 4 + 3 + 5x + -6x = 8 + -1(7x + -1) * x Combine like terms: 4 + 3 = 7 7 + 5x + -6x = 8 + -1(7x + -1) * x Combine like terms: 5x + -6x = -1x 7 + -1x = 8 + -1(7x + -1) * x Reorder the terms: 7 + -1x = 8 + -1(-1 + 7x) * x Reorder the terms for easier multiplication: 7 + -1x = 8 + -1x(-1 + 7x) 7 + -1x = 8 + (-1 * -1x + 7x * -1x) 7 + -1x = 8 + (1x + -7x2) Solving 7 + -1x = 8 + 1x + -7x2 Solving for variable 'x'. Reorder the terms: 7 + -8 + -1x + -1x + 7x2 = 8 + 1x + -7x2 + -8 + -1x + 7x2 Combine like terms: 7 + -8 = -1 -1 + -1x + -1x + 7x2 = 8 + 1x + -7x2 + -8 + -1x + 7x2 Combine like terms: -1x + -1x = -2x -1 + -2x + 7x2 = 8 + 1x + -7x2 + -8 + -1x + 7x2 Reorder the terms: -1 + -2x + 7x2 = 8 + -8 + 1x + -1x + -7x2 + 7x2 Combine like terms: 8 + -8 = 0 -1 + -2x + 7x2 = 0 + 1x + -1x + -7x2 + 7x2 -1 + -2x + 7x2 = 1x + -1x + -7x2 + 7x2 Combine like terms: 1x + -1x = 0 -1 + -2x + 7x2 = 0 + -7x2 + 7x2 -1 + -2x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 -1 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.1428571429 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + -0.2857142857x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + -0.2857142857x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + 0.1428571429 -0.2857142857x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 -0.2857142857x + x2 = 0.1428571429 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.1428571429 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.1428571429 + 0.02040816328 Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618 0.02040816328 + -0.2857142857x + x2 = 0.16326530618 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.16326530618 Calculate the square root of the right side: 0.404061018 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.404061018 and -0.404061018.Subproblem 1
x + -0.1428571429 = 0.404061018 Simplifying x + -0.1428571429 = 0.404061018 Reorder the terms: -0.1428571429 + x = 0.404061018 Solving -0.1428571429 + x = 0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.404061018 + 0.1428571429 x = 0.404061018 + 0.1428571429 Combine like terms: 0.404061018 + 0.1428571429 = 0.5469181609 x = 0.5469181609 Simplifying x = 0.5469181609Subproblem 2
x + -0.1428571429 = -0.404061018 Simplifying x + -0.1428571429 = -0.404061018 Reorder the terms: -0.1428571429 + x = -0.404061018 Solving -0.1428571429 + x = -0.404061018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.404061018 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.404061018 + 0.1428571429 x = -0.404061018 + 0.1428571429 Combine like terms: -0.404061018 + 0.1428571429 = -0.2612038751 x = -0.2612038751 Simplifying x = -0.2612038751Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5469181609, -0.2612038751}
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