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Simplifying (x2) + -1(20x) + 1 = 0 x2 + -1(20x) + 1 = 0 Remove parenthesis around (20x) x2 + -1 * 20x + 1 = 0 Multiply -1 * 20 x2 + -20x + 1 = 0 Reorder the terms: 1 + -20x + x2 = 0 Solving 1 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -20x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -20x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -20x + x2 = 0 + -1 -20x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -20x + x2 = -1 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -1 + 100 Reorder the terms: 100 + -20x + x2 = -1 + 100 Combine like terms: -1 + 100 = 99 100 + -20x + x2 = 99 Factor a perfect square on the left side: (x + -10)(x + -10) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + -10) equal to 9.949874371 and -9.949874371.Subproblem 1
x + -10 = 9.949874371 Simplifying x + -10 = 9.949874371 Reorder the terms: -10 + x = 9.949874371 Solving -10 + x = 9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.949874371 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.949874371 + 10 x = 9.949874371 + 10 Combine like terms: 9.949874371 + 10 = 19.949874371 x = 19.949874371 Simplifying x = 19.949874371Subproblem 2
x + -10 = -9.949874371 Simplifying x + -10 = -9.949874371 Reorder the terms: -10 + x = -9.949874371 Solving -10 + x = -9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.949874371 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.949874371 + 10 x = -9.949874371 + 10 Combine like terms: -9.949874371 + 10 = 0.050125629 x = 0.050125629 Simplifying x = 0.050125629Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.949874371, 0.050125629}
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