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Simplifying x2 + 20x = -33 Reorder the terms: 20x + x2 = -33 Solving 20x + x2 = -33 Solving for variable 'x'. Reorder the terms: 33 + 20x + x2 = -33 + 33 Combine like terms: -33 + 33 = 0 33 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 20x + -33 + x2 = 0 + -33 Reorder the terms: 33 + -33 + 20x + x2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 20x + x2 = 0 + -33 20x + x2 = 0 + -33 Combine like terms: 0 + -33 = -33 20x + x2 = -33 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 = -33 + 100 Reorder the terms: 100 + 20x + x2 = -33 + 100 Combine like terms: -33 + 100 = 67 100 + 20x + x2 = 67 Factor a perfect square on the left side: (x + 10)(x + 10) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + 10) equal to 8.185352772 and -8.185352772.Subproblem 1
x + 10 = 8.185352772 Simplifying x + 10 = 8.185352772 Reorder the terms: 10 + x = 8.185352772 Solving 10 + x = 8.185352772 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 = 8.185352772 + -10 Combine like terms: 10 + -10 = 0 0 + x = 8.185352772 + -10 x = 8.185352772 + -10 Combine like terms: 8.185352772 + -10 = -1.814647228 x = -1.814647228 Simplifying x = -1.814647228Subproblem 2
x + 10 = -8.185352772 Simplifying x + 10 = -8.185352772 Reorder the terms: 10 + x = -8.185352772 Solving 10 + x = -8.185352772 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 = -8.185352772 + -10 Combine like terms: 10 + -10 = 0 0 + x = -8.185352772 + -10 x = -8.185352772 + -10 Combine like terms: -8.185352772 + -10 = -18.185352772 x = -18.185352772 Simplifying x = -18.185352772Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.814647228, -18.185352772}
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