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Simplifying 20x2 + 11x + -2 = 0 Reorder the terms: -2 + 11x + 20x2 = 0 Solving -2 + 11x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.1 + 0.55x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.55x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.55x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.55x + x2 = 0 + 0.1 0.55x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.55x + x2 = 0.1 The x term is 0.55x. Take half its coefficient (0.275). Square it (0.075625) and add it to both sides. Add '0.075625' to each side of the equation. 0.55x + 0.075625 + x2 = 0.1 + 0.075625 Reorder the terms: 0.075625 + 0.55x + x2 = 0.1 + 0.075625 Combine like terms: 0.1 + 0.075625 = 0.175625 0.075625 + 0.55x + x2 = 0.175625 Factor a perfect square on the left side: (x + 0.275)(x + 0.275) = 0.175625 Calculate the square root of the right side: 0.419076365 Break this problem into two subproblems by setting (x + 0.275) equal to 0.419076365 and -0.419076365.Subproblem 1
x + 0.275 = 0.419076365 Simplifying x + 0.275 = 0.419076365 Reorder the terms: 0.275 + x = 0.419076365 Solving 0.275 + x = 0.419076365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + x = 0.419076365 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = 0.419076365 + -0.275 x = 0.419076365 + -0.275 Combine like terms: 0.419076365 + -0.275 = 0.144076365 x = 0.144076365 Simplifying x = 0.144076365Subproblem 2
x + 0.275 = -0.419076365 Simplifying x + 0.275 = -0.419076365 Reorder the terms: 0.275 + x = -0.419076365 Solving 0.275 + x = -0.419076365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.275' to each side of the equation. 0.275 + -0.275 + x = -0.419076365 + -0.275 Combine like terms: 0.275 + -0.275 = 0.000 0.000 + x = -0.419076365 + -0.275 x = -0.419076365 + -0.275 Combine like terms: -0.419076365 + -0.275 = -0.694076365 x = -0.694076365 Simplifying x = -0.694076365Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.144076365, -0.694076365}
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