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Simplifying x2 + 20x + 85 = 0 Reorder the terms: 85 + 20x + x2 = 0 Solving 85 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-85' to each side of the equation. 85 + 20x + -85 + x2 = 0 + -85 Reorder the terms: 85 + -85 + 20x + x2 = 0 + -85 Combine like terms: 85 + -85 = 0 0 + 20x + x2 = 0 + -85 20x + x2 = 0 + -85 Combine like terms: 0 + -85 = -85 20x + x2 = -85 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 = -85 + 100 Reorder the terms: 100 + 20x + x2 = -85 + 100 Combine like terms: -85 + 100 = 15 100 + 20x + x2 = 15 Factor a perfect square on the left side: (x + 10)(x + 10) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 10) equal to 3.872983346 and -3.872983346.Subproblem 1
x + 10 = 3.872983346 Simplifying x + 10 = 3.872983346 Reorder the terms: 10 + x = 3.872983346 Solving 10 + x = 3.872983346 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 = 3.872983346 + -10 Combine like terms: 10 + -10 = 0 0 + x = 3.872983346 + -10 x = 3.872983346 + -10 Combine like terms: 3.872983346 + -10 = -6.127016654 x = -6.127016654 Simplifying x = -6.127016654Subproblem 2
x + 10 = -3.872983346 Simplifying x + 10 = -3.872983346 Reorder the terms: 10 + x = -3.872983346 Solving 10 + x = -3.872983346 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 = -3.872983346 + -10 Combine like terms: 10 + -10 = 0 0 + x = -3.872983346 + -10 x = -3.872983346 + -10 Combine like terms: -3.872983346 + -10 = -13.872983346 x = -13.872983346 Simplifying x = -13.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.127016654, -13.872983346}
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