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Simplifying (14x2) + 13x + -2 = 0 Reorder the terms: -2 + 13x + (14x2) = 0 Solving -2 + 13x + (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'. -0.1428571429 + 0.9285714286x + x2 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.9285714286x + 0.1428571429 + x2 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.9285714286x + x2 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.9285714286x + x2 = 0 + 0.1428571429 0.9285714286x + x2 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.9285714286x + x2 = 0.1428571429 The x term is 0.9285714286x. Take half its coefficient (0.4642857143). Square it (0.2155612245) and add it to both sides. Add '0.2155612245' to each side of the equation. 0.9285714286x + 0.2155612245 + x2 = 0.1428571429 + 0.2155612245 Reorder the terms: 0.2155612245 + 0.9285714286x + x2 = 0.1428571429 + 0.2155612245 Combine like terms: 0.1428571429 + 0.2155612245 = 0.3584183674 0.2155612245 + 0.9285714286x + x2 = 0.3584183674 Factor a perfect square on the left side: ((x) + 0.4642857143)((x) + 0.4642857143) = 0.3584183674 Calculate the square root of the right side: 0.598680522 Break this problem into two subproblems by setting ((x) + 0.4642857143) equal to 0.598680522 and -0.598680522.Subproblem 1
(x) + 0.4642857143 = 0.598680522 Simplifying (x) + 0.4642857143 = 0.598680522 x + 0.4642857143 = 0.598680522 Reorder the terms: 0.4642857143 + x = 0.598680522 Solving 0.4642857143 + x = 0.598680522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + x = 0.598680522 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + x = 0.598680522 + -0.4642857143 x = 0.598680522 + -0.4642857143 Combine like terms: 0.598680522 + -0.4642857143 = 0.1343948077 x = 0.1343948077 Simplifying x = 0.1343948077Subproblem 2
(x) + 0.4642857143 = -0.598680522 Simplifying (x) + 0.4642857143 = -0.598680522 x + 0.4642857143 = -0.598680522 Reorder the terms: 0.4642857143 + x = -0.598680522 Solving 0.4642857143 + x = -0.598680522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + x = -0.598680522 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + x = -0.598680522 + -0.4642857143 x = -0.598680522 + -0.4642857143 Combine like terms: -0.598680522 + -0.4642857143 = -1.0629662363 x = -1.0629662363 Simplifying x = -1.0629662363Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1343948077, -1.0629662363}
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