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Simplifying 14x2 + 4x + -13 = 0 Reorder the terms: -13 + 4x + 14x2 = 0 Solving -13 + 4x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.9285714286 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.9285714286' to each side of the equation. -0.9285714286 + 0.2857142857x + 0.9285714286 + x2 = 0 + 0.9285714286 Reorder the terms: -0.9285714286 + 0.9285714286 + 0.2857142857x + x2 = 0 + 0.9285714286 Combine like terms: -0.9285714286 + 0.9285714286 = 0.0000000000 0.0000000000 + 0.2857142857x + x2 = 0 + 0.9285714286 0.2857142857x + x2 = 0 + 0.9285714286 Combine like terms: 0 + 0.9285714286 = 0.9285714286 0.2857142857x + x2 = 0.9285714286 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 = 0.9285714286 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 0.9285714286 + 0.02040816328 Combine like terms: 0.9285714286 + 0.02040816328 = 0.94897959188 0.02040816328 + 0.2857142857x + x2 = 0.94897959188 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 0.94897959188 Calculate the square root of the right side: 0.974155836 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 0.974155836 and -0.974155836.Subproblem 1
x + 0.1428571429 = 0.974155836 Simplifying x + 0.1428571429 = 0.974155836 Reorder the terms: 0.1428571429 + x = 0.974155836 Solving 0.1428571429 + x = 0.974155836 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 = 0.974155836 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 0.974155836 + -0.1428571429 x = 0.974155836 + -0.1428571429 Combine like terms: 0.974155836 + -0.1428571429 = 0.8312986931 x = 0.8312986931 Simplifying x = 0.8312986931Subproblem 2
x + 0.1428571429 = -0.974155836 Simplifying x + 0.1428571429 = -0.974155836 Reorder the terms: 0.1428571429 + x = -0.974155836 Solving 0.1428571429 + x = -0.974155836 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 = -0.974155836 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -0.974155836 + -0.1428571429 x = -0.974155836 + -0.1428571429 Combine like terms: -0.974155836 + -0.1428571429 = -1.1170129789 x = -1.1170129789 Simplifying x = -1.1170129789Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8312986931, -1.1170129789}
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