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Simplifying 14x2 + x + 3 = 0 Reorder the terms: 3 + x + 14x2 = 0 Solving 3 + 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'. 0.2142857143 + 0.07142857143x + x2 = 0 Move the constant term to the right: Add '-0.2142857143' to each side of the equation. 0.2142857143 + 0.07142857143x + -0.2142857143 + x2 = 0 + -0.2142857143 Reorder the terms: 0.2142857143 + -0.2142857143 + 0.07142857143x + x2 = 0 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + 0.07142857143x + x2 = 0 + -0.2142857143 0.07142857143x + x2 = 0 + -0.2142857143 Combine like terms: 0 + -0.2142857143 = -0.2142857143 0.07142857143x + x2 = -0.2142857143 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 = -0.2142857143 + 0.25 Reorder the terms: 0.25 + 0.07142857143x + x2 = -0.2142857143 + 0.25 Combine like terms: -0.2142857143 + 0.25 = 0.0357142857 0.25 + 0.07142857143x + x2 = 0.0357142857 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.0357142857 Calculate the square root of the right side: 0.188982236 Break this problem into two subproblems by setting (x + 0.5) equal to 0.188982236 and -0.188982236.Subproblem 1
x + 0.5 = 0.188982236 Simplifying x + 0.5 = 0.188982236 Reorder the terms: 0.5 + x = 0.188982236 Solving 0.5 + x = 0.188982236 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 = 0.188982236 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.188982236 + -0.5 x = 0.188982236 + -0.5 Combine like terms: 0.188982236 + -0.5 = -0.311017764 x = -0.311017764 Simplifying x = -0.311017764Subproblem 2
x + 0.5 = -0.188982236 Simplifying x + 0.5 = -0.188982236 Reorder the terms: 0.5 + x = -0.188982236 Solving 0.5 + x = -0.188982236 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 = -0.188982236 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.188982236 + -0.5 x = -0.188982236 + -0.5 Combine like terms: -0.188982236 + -0.5 = -0.688982236 x = -0.688982236 Simplifying x = -0.688982236Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.311017764, -0.688982236}
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