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Simplifying x2 + 20x + 53 = 0 Reorder the terms: 53 + 20x + x2 = 0 Solving 53 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 20x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 20x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 20x + x2 = 0 + -53 20x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 20x + x2 = -53 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 = -53 + 100 Reorder the terms: 100 + 20x + x2 = -53 + 100 Combine like terms: -53 + 100 = 47 100 + 20x + x2 = 47 Factor a perfect square on the left side: (x + 10)(x + 10) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + 10) equal to 6.8556546 and -6.8556546.Subproblem 1
x + 10 = 6.8556546 Simplifying x + 10 = 6.8556546 Reorder the terms: 10 + x = 6.8556546 Solving 10 + x = 6.8556546 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 = 6.8556546 + -10 Combine like terms: 10 + -10 = 0 0 + x = 6.8556546 + -10 x = 6.8556546 + -10 Combine like terms: 6.8556546 + -10 = -3.1443454 x = -3.1443454 Simplifying x = -3.1443454Subproblem 2
x + 10 = -6.8556546 Simplifying x + 10 = -6.8556546 Reorder the terms: 10 + x = -6.8556546 Solving 10 + x = -6.8556546 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 = -6.8556546 + -10 Combine like terms: 10 + -10 = 0 0 + x = -6.8556546 + -10 x = -6.8556546 + -10 Combine like terms: -6.8556546 + -10 = -16.8556546 x = -16.8556546 Simplifying x = -16.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.1443454, -16.8556546}
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