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Simplifying 20x2 + 21x + 2 = 0 Reorder the terms: 2 + 21x + 20x2 = 0 Solving 2 + 21x + 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 + 1.05x + x2 = 0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + 1.05x + -0.1 + x2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + 1.05x + x2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + 1.05x + x2 = 0 + -0.1 1.05x + x2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 1.05x + x2 = -0.1 The x term is 1.05x. Take half its coefficient (0.525). Square it (0.275625) and add it to both sides. Add '0.275625' to each side of the equation. 1.05x + 0.275625 + x2 = -0.1 + 0.275625 Reorder the terms: 0.275625 + 1.05x + x2 = -0.1 + 0.275625 Combine like terms: -0.1 + 0.275625 = 0.175625 0.275625 + 1.05x + x2 = 0.175625 Factor a perfect square on the left side: (x + 0.525)(x + 0.525) = 0.175625 Calculate the square root of the right side: 0.419076365 Break this problem into two subproblems by setting (x + 0.525) equal to 0.419076365 and -0.419076365.Subproblem 1
x + 0.525 = 0.419076365 Simplifying x + 0.525 = 0.419076365 Reorder the terms: 0.525 + x = 0.419076365 Solving 0.525 + x = 0.419076365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = 0.419076365 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = 0.419076365 + -0.525 x = 0.419076365 + -0.525 Combine like terms: 0.419076365 + -0.525 = -0.105923635 x = -0.105923635 Simplifying x = -0.105923635Subproblem 2
x + 0.525 = -0.419076365 Simplifying x + 0.525 = -0.419076365 Reorder the terms: 0.525 + x = -0.419076365 Solving 0.525 + x = -0.419076365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.525' to each side of the equation. 0.525 + -0.525 + x = -0.419076365 + -0.525 Combine like terms: 0.525 + -0.525 = 0.000 0.000 + x = -0.419076365 + -0.525 x = -0.419076365 + -0.525 Combine like terms: -0.419076365 + -0.525 = -0.944076365 x = -0.944076365 Simplifying x = -0.944076365Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.105923635, -0.944076365}
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