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Simplifying x2 + -40x + 333 = 0 Reorder the terms: 333 + -40x + x2 = 0 Solving 333 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-333' to each side of the equation. 333 + -40x + -333 + x2 = 0 + -333 Reorder the terms: 333 + -333 + -40x + x2 = 0 + -333 Combine like terms: 333 + -333 = 0 0 + -40x + x2 = 0 + -333 -40x + x2 = 0 + -333 Combine like terms: 0 + -333 = -333 -40x + x2 = -333 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -333 + 400 Reorder the terms: 400 + -40x + x2 = -333 + 400 Combine like terms: -333 + 400 = 67 400 + -40x + x2 = 67 Factor a perfect square on the left side: (x + -20)(x + -20) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + -20) equal to 8.185352772 and -8.185352772.Subproblem 1
x + -20 = 8.185352772 Simplifying x + -20 = 8.185352772 Reorder the terms: -20 + x = 8.185352772 Solving -20 + x = 8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 8.185352772 + 20 Combine like terms: -20 + 20 = 0 0 + x = 8.185352772 + 20 x = 8.185352772 + 20 Combine like terms: 8.185352772 + 20 = 28.185352772 x = 28.185352772 Simplifying x = 28.185352772Subproblem 2
x + -20 = -8.185352772 Simplifying x + -20 = -8.185352772 Reorder the terms: -20 + x = -8.185352772 Solving -20 + x = -8.185352772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -8.185352772 + 20 Combine like terms: -20 + 20 = 0 0 + x = -8.185352772 + 20 x = -8.185352772 + 20 Combine like terms: -8.185352772 + 20 = 11.814647228 x = 11.814647228 Simplifying x = 11.814647228Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.185352772, 11.814647228}
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