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Simplifying (4x2 + -2x + -58) + (3x2 + 4x) = 0 Reorder the terms: (-58 + -2x + 4x2) + (3x2 + 4x) = 0 Remove parenthesis around (-58 + -2x + 4x2) -58 + -2x + 4x2 + (3x2 + 4x) = 0 Reorder the terms: -58 + -2x + 4x2 + (4x + 3x2) = 0 Remove parenthesis around (4x + 3x2) -58 + -2x + 4x2 + 4x + 3x2 = 0 Reorder the terms: -58 + -2x + 4x + 4x2 + 3x2 = 0 Combine like terms: -2x + 4x = 2x -58 + 2x + 4x2 + 3x2 = 0 Combine like terms: 4x2 + 3x2 = 7x2 -58 + 2x + 7x2 = 0 Solving -58 + 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'. -8.285714286 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '8.285714286' to each side of the equation. -8.285714286 + 0.2857142857x + 8.285714286 + x2 = 0 + 8.285714286 Reorder the terms: -8.285714286 + 8.285714286 + 0.2857142857x + x2 = 0 + 8.285714286 Combine like terms: -8.285714286 + 8.285714286 = 0.000000000 0.000000000 + 0.2857142857x + x2 = 0 + 8.285714286 0.2857142857x + x2 = 0 + 8.285714286 Combine like terms: 0 + 8.285714286 = 8.285714286 0.2857142857x + x2 = 8.285714286 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 = 8.285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 8.285714286 + 0.02040816328 Combine like terms: 8.285714286 + 0.02040816328 = 8.30612244928 0.02040816328 + 0.2857142857x + x2 = 8.30612244928 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 8.30612244928 Calculate the square root of the right side: 2.882034429 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 2.882034429 and -2.882034429.Subproblem 1
x + 0.1428571429 = 2.882034429 Simplifying x + 0.1428571429 = 2.882034429 Reorder the terms: 0.1428571429 + x = 2.882034429 Solving 0.1428571429 + x = 2.882034429 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 = 2.882034429 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 2.882034429 + -0.1428571429 x = 2.882034429 + -0.1428571429 Combine like terms: 2.882034429 + -0.1428571429 = 2.7391772861 x = 2.7391772861 Simplifying x = 2.7391772861Subproblem 2
x + 0.1428571429 = -2.882034429 Simplifying x + 0.1428571429 = -2.882034429 Reorder the terms: 0.1428571429 + x = -2.882034429 Solving 0.1428571429 + x = -2.882034429 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 = -2.882034429 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -2.882034429 + -0.1428571429 x = -2.882034429 + -0.1428571429 Combine like terms: -2.882034429 + -0.1428571429 = -3.0248915719 x = -3.0248915719 Simplifying x = -3.0248915719Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7391772861, -3.0248915719}
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