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Simplifying 7x2 + x + 1 = 0 Reorder the terms: 1 + x + 7x2 = 0 Solving 1 + x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 0.1428571429x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.1428571429x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.1428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.1428571429x + x2 = 0 + -0.1428571429 0.1428571429x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.1428571429x + x2 = -0.1428571429 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. 0.1428571429x + 0.25 + x2 = -0.1428571429 + 0.25 Reorder the terms: 0.25 + 0.1428571429x + x2 = -0.1428571429 + 0.25 Combine like terms: -0.1428571429 + 0.25 = 0.1071428571 0.25 + 0.1428571429x + x2 = 0.1071428571 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.1071428571 Calculate the square root of the right side: 0.327326835 Break this problem into two subproblems by setting (x + 0.5) equal to 0.327326835 and -0.327326835.Subproblem 1
x + 0.5 = 0.327326835 Simplifying x + 0.5 = 0.327326835 Reorder the terms: 0.5 + x = 0.327326835 Solving 0.5 + x = 0.327326835 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 = 0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.327326835 + -0.5 x = 0.327326835 + -0.5 Combine like terms: 0.327326835 + -0.5 = -0.172673165 x = -0.172673165 Simplifying x = -0.172673165Subproblem 2
x + 0.5 = -0.327326835 Simplifying x + 0.5 = -0.327326835 Reorder the terms: 0.5 + x = -0.327326835 Solving 0.5 + x = -0.327326835 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 = -0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.327326835 + -0.5 x = -0.327326835 + -0.5 Combine like terms: -0.327326835 + -0.5 = -0.827326835 x = -0.827326835 Simplifying x = -0.827326835Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.172673165, -0.827326835}
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