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Simplifying (3x2 + -5x + -1) + (4x2 + 7x + -1) = 0 Reorder the terms: (-1 + -5x + 3x2) + (4x2 + 7x + -1) = 0 Remove parenthesis around (-1 + -5x + 3x2) -1 + -5x + 3x2 + (4x2 + 7x + -1) = 0 Reorder the terms: -1 + -5x + 3x2 + (-1 + 7x + 4x2) = 0 Remove parenthesis around (-1 + 7x + 4x2) -1 + -5x + 3x2 + -1 + 7x + 4x2 = 0 Reorder the terms: -1 + -1 + -5x + 7x + 3x2 + 4x2 = 0 Combine like terms: -1 + -1 = -2 -2 + -5x + 7x + 3x2 + 4x2 = 0 Combine like terms: -5x + 7x = 2x -2 + 2x + 3x2 + 4x2 = 0 Combine like terms: 3x2 + 4x2 = 7x2 -2 + 2x + 7x2 = 0 Solving -2 + 2x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857x + 0.2857142857 + x2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + 0.2857142857x + x2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + 0.2857142857 0.2857142857x + x2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 0.2857142857x + x2 = 0.2857142857 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 = 0.2857142857 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.2857142857 + 0.02040816328 Combine like terms: 0.2857142857 + 0.02040816328 = 0.30612244898 0.02040816328 + 0.2857142857x + x2 = 0.30612244898 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.30612244898 Calculate the square root of the right side: 0.553283335 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.553283335 and -0.553283335.Subproblem 1
x + 0.1428571429 = 0.553283335 Simplifying x + 0.1428571429 = 0.553283335 Reorder the terms: 0.1428571429 + x = 0.553283335 Solving 0.1428571429 + x = 0.553283335 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 = 0.553283335 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.553283335 + -0.1428571429 x = 0.553283335 + -0.1428571429 Combine like terms: 0.553283335 + -0.1428571429 = 0.4104261921 x = 0.4104261921 Simplifying x = 0.4104261921Subproblem 2
x + 0.1428571429 = -0.553283335 Simplifying x + 0.1428571429 = -0.553283335 Reorder the terms: 0.1428571429 + x = -0.553283335 Solving 0.1428571429 + x = -0.553283335 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 = -0.553283335 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.553283335 + -0.1428571429 x = -0.553283335 + -0.1428571429 Combine like terms: -0.553283335 + -0.1428571429 = -0.6961404779 x = -0.6961404779 Simplifying x = -0.6961404779Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4104261921, -0.6961404779}
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