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Simplifying 14x2 + 2x + -21 = 0 Reorder the terms: -21 + 2x + 14x2 = 0 Solving -21 + 2x + 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'. -1.5 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 0.1428571429x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 0.1428571429x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 0.1428571429x + x2 = 0 + 1.5 0.1428571429x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 0.1428571429x + x2 = 1.5 The x term is 0.1428571429x. Take half its coefficient (0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. 0.1428571429x + 0.005102040819 + x2 = 1.5 + 0.005102040819 Reorder the terms: 0.005102040819 + 0.1428571429x + x2 = 1.5 + 0.005102040819 Combine like terms: 1.5 + 0.005102040819 = 1.505102040819 0.005102040819 + 0.1428571429x + x2 = 1.505102040819 Factor a perfect square on the left side: (x + 0.07142857145)(x + 0.07142857145) = 1.505102040819 Calculate the square root of the right side: 1.226826003 Break this problem into two subproblems by setting (x + 0.07142857145) equal to 1.226826003 and -1.226826003.Subproblem 1
x + 0.07142857145 = 1.226826003 Simplifying x + 0.07142857145 = 1.226826003 Reorder the terms: 0.07142857145 + x = 1.226826003 Solving 0.07142857145 + x = 1.226826003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = 1.226826003 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 1.226826003 + -0.07142857145 x = 1.226826003 + -0.07142857145 Combine like terms: 1.226826003 + -0.07142857145 = 1.15539743155 x = 1.15539743155 Simplifying x = 1.15539743155Subproblem 2
x + 0.07142857145 = -1.226826003 Simplifying x + 0.07142857145 = -1.226826003 Reorder the terms: 0.07142857145 + x = -1.226826003 Solving 0.07142857145 + x = -1.226826003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.07142857145' to each side of the equation. 0.07142857145 + -0.07142857145 + x = -1.226826003 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -1.226826003 + -0.07142857145 x = -1.226826003 + -0.07142857145 Combine like terms: -1.226826003 + -0.07142857145 = -1.29825457445 x = -1.29825457445 Simplifying x = -1.29825457445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.15539743155, -1.29825457445}
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