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Simplifying 14x2 + x + 1 = 0 Reorder the terms: 1 + x + 14x2 = 0 Solving 1 + x + 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'. 0.07142857143 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '-0.07142857143' to each side of the equation. 0.07142857143 + 0.07142857143x + -0.07142857143 + x2 = 0 + -0.07142857143 Reorder the terms: 0.07142857143 + -0.07142857143 + 0.07142857143x + x2 = 0 + -0.07142857143 Combine like terms: 0.07142857143 + -0.07142857143 = 0.00000000000 0.00000000000 + 0.07142857143x + x2 = 0 + -0.07142857143 0.07142857143x + x2 = 0 + -0.07142857143 Combine like terms: 0 + -0.07142857143 = -0.07142857143 0.07142857143x + x2 = -0.07142857143 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.07142857143x + 0.25 + x2 = -0.07142857143 + 0.25 Reorder the terms: 0.25 + 0.07142857143x + x2 = -0.07142857143 + 0.25 Combine like terms: -0.07142857143 + 0.25 = 0.17857142857 0.25 + 0.07142857143x + x2 = 0.17857142857 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.17857142857 Calculate the square root of the right side: 0.422577127 Break this problem into two subproblems by setting (x + 0.5) equal to 0.422577127 and -0.422577127.Subproblem 1
x + 0.5 = 0.422577127 Simplifying x + 0.5 = 0.422577127 Reorder the terms: 0.5 + x = 0.422577127 Solving 0.5 + x = 0.422577127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.422577127 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.422577127 + -0.5 x = 0.422577127 + -0.5 Combine like terms: 0.422577127 + -0.5 = -0.077422873 x = -0.077422873 Simplifying x = -0.077422873Subproblem 2
x + 0.5 = -0.422577127 Simplifying x + 0.5 = -0.422577127 Reorder the terms: 0.5 + x = -0.422577127 Solving 0.5 + x = -0.422577127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.422577127 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.422577127 + -0.5 x = -0.422577127 + -0.5 Combine like terms: -0.422577127 + -0.5 = -0.922577127 x = -0.922577127 Simplifying x = -0.922577127Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.077422873, -0.922577127}
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