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Simplifying 20x2 + 19x + -181 = 0 Reorder the terms: -181 + 19x + 20x2 = 0 Solving -181 + 19x + 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'. -9.05 + 0.95x + x2 = 0 Move the constant term to the right: Add '9.05' to each side of the equation. -9.05 + 0.95x + 9.05 + x2 = 0 + 9.05 Reorder the terms: -9.05 + 9.05 + 0.95x + x2 = 0 + 9.05 Combine like terms: -9.05 + 9.05 = 0.00 0.00 + 0.95x + x2 = 0 + 9.05 0.95x + x2 = 0 + 9.05 Combine like terms: 0 + 9.05 = 9.05 0.95x + x2 = 9.05 The x term is 0.95x. Take half its coefficient (0.475). Square it (0.225625) and add it to both sides. Add '0.225625' to each side of the equation. 0.95x + 0.225625 + x2 = 9.05 + 0.225625 Reorder the terms: 0.225625 + 0.95x + x2 = 9.05 + 0.225625 Combine like terms: 9.05 + 0.225625 = 9.275625 0.225625 + 0.95x + x2 = 9.275625 Factor a perfect square on the left side: (x + 0.475)(x + 0.475) = 9.275625 Calculate the square root of the right side: 3.045591076 Break this problem into two subproblems by setting (x + 0.475) equal to 3.045591076 and -3.045591076.Subproblem 1
x + 0.475 = 3.045591076 Simplifying x + 0.475 = 3.045591076 Reorder the terms: 0.475 + x = 3.045591076 Solving 0.475 + x = 3.045591076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.475' to each side of the equation. 0.475 + -0.475 + x = 3.045591076 + -0.475 Combine like terms: 0.475 + -0.475 = 0.000 0.000 + x = 3.045591076 + -0.475 x = 3.045591076 + -0.475 Combine like terms: 3.045591076 + -0.475 = 2.570591076 x = 2.570591076 Simplifying x = 2.570591076Subproblem 2
x + 0.475 = -3.045591076 Simplifying x + 0.475 = -3.045591076 Reorder the terms: 0.475 + x = -3.045591076 Solving 0.475 + x = -3.045591076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.475' to each side of the equation. 0.475 + -0.475 + x = -3.045591076 + -0.475 Combine like terms: 0.475 + -0.475 = 0.000 0.000 + x = -3.045591076 + -0.475 x = -3.045591076 + -0.475 Combine like terms: -3.045591076 + -0.475 = -3.520591076 x = -3.520591076 Simplifying x = -3.520591076Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.570591076, -3.520591076}
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