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Simplifying (-20x2) + 19x + 2 = 0 Reorder the terms: 2 + 19x + (-20x2) = 0 Solving 2 + 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'. -0.1 + -0.95x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + -0.95x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + -0.95x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + -0.95x + x2 = 0 + 0.1 -0.95x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 -0.95x + x2 = 0.1 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 = 0.1 + 0.225625 Reorder the terms: 0.225625 + -0.95x + x2 = 0.1 + 0.225625 Combine like terms: 0.1 + 0.225625 = 0.325625 0.225625 + -0.95x + x2 = 0.325625 Factor a perfect square on the left side: ((x) + -0.475)((x) + -0.475) = 0.325625 Calculate the square root of the right side: 0.570635611 Break this problem into two subproblems by setting ((x) + -0.475) equal to 0.570635611 and -0.570635611.Subproblem 1
(x) + -0.475 = 0.570635611 Simplifying (x) + -0.475 = 0.570635611 x + -0.475 = 0.570635611 Reorder the terms: -0.475 + x = 0.570635611 Solving -0.475 + x = 0.570635611 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 = 0.570635611 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + x = 0.570635611 + 0.475 x = 0.570635611 + 0.475 Combine like terms: 0.570635611 + 0.475 = 1.045635611 x = 1.045635611 Simplifying x = 1.045635611Subproblem 2
(x) + -0.475 = -0.570635611 Simplifying (x) + -0.475 = -0.570635611 x + -0.475 = -0.570635611 Reorder the terms: -0.475 + x = -0.570635611 Solving -0.475 + x = -0.570635611 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 = -0.570635611 + 0.475 Combine like terms: -0.475 + 0.475 = 0.000 0.000 + x = -0.570635611 + 0.475 x = -0.570635611 + 0.475 Combine like terms: -0.570635611 + 0.475 = -0.095635611 x = -0.095635611 Simplifying x = -0.095635611Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.045635611, -0.095635611}
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