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Simplifying x2 + 20x = -1 Reorder the terms: 20x + x2 = -1 Solving 20x + x2 = -1 Solving for variable 'x'. Reorder the terms: 1 + 20x + x2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 20x + x2 = 0 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 = -0.050125629 x = -0.050125629 Simplifying x = -0.050125629Subproblem 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 = -19.949874371 x = -19.949874371 Simplifying x = -19.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.050125629, -19.949874371}
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