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Simplifying x2 + 20x + 59 = 0 Reorder the terms: 59 + 20x + x2 = 0 Solving 59 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 20x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 20x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 20x + x2 = 0 + -59 20x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 20x + x2 = -59 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 = -59 + 100 Reorder the terms: 100 + 20x + x2 = -59 + 100 Combine like terms: -59 + 100 = 41 100 + 20x + x2 = 41 Factor a perfect square on the left side: (x + 10)(x + 10) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 10) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 10 = 6.403124237 Simplifying x + 10 = 6.403124237 Reorder the terms: 10 + x = 6.403124237 Solving 10 + x = 6.403124237 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 = 6.403124237 + -10 Combine like terms: 10 + -10 = 0 0 + x = 6.403124237 + -10 x = 6.403124237 + -10 Combine like terms: 6.403124237 + -10 = -3.596875763 x = -3.596875763 Simplifying x = -3.596875763Subproblem 2
x + 10 = -6.403124237 Simplifying x + 10 = -6.403124237 Reorder the terms: 10 + x = -6.403124237 Solving 10 + x = -6.403124237 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 = -6.403124237 + -10 Combine like terms: 10 + -10 = 0 0 + x = -6.403124237 + -10 x = -6.403124237 + -10 Combine like terms: -6.403124237 + -10 = -16.403124237 x = -16.403124237 Simplifying x = -16.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.596875763, -16.403124237}
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