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Simplifying x2 + x = 553 Reorder the terms: x + x2 = 553 Solving x + x2 = 553 Solving for variable 'x'. Reorder the terms: -553 + x + x2 = 553 + -553 Combine like terms: 553 + -553 = 0 -553 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '553' to each side of the equation. -553 + x + 553 + x2 = 0 + 553 Reorder the terms: -553 + 553 + x + x2 = 0 + 553 Combine like terms: -553 + 553 = 0 0 + x + x2 = 0 + 553 x + x2 = 0 + 553 Combine like terms: 0 + 553 = 553 x + x2 = 553 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 553 + 0.25 Reorder the terms: 0.25 + x + x2 = 553 + 0.25 Combine like terms: 553 + 0.25 = 553.25 0.25 + x + x2 = 553.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 553.25 Calculate the square root of the right side: 23.521266973 Break this problem into two subproblems by setting (x + 0.5) equal to 23.521266973 and -23.521266973.Subproblem 1
x + 0.5 = 23.521266973 Simplifying x + 0.5 = 23.521266973 Reorder the terms: 0.5 + x = 23.521266973 Solving 0.5 + x = 23.521266973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 23.521266973 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 23.521266973 + -0.5 x = 23.521266973 + -0.5 Combine like terms: 23.521266973 + -0.5 = 23.021266973 x = 23.021266973 Simplifying x = 23.021266973Subproblem 2
x + 0.5 = -23.521266973 Simplifying x + 0.5 = -23.521266973 Reorder the terms: 0.5 + x = -23.521266973 Solving 0.5 + x = -23.521266973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -23.521266973 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -23.521266973 + -0.5 x = -23.521266973 + -0.5 Combine like terms: -23.521266973 + -0.5 = -24.021266973 x = -24.021266973 Simplifying x = -24.021266973Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.021266973, -24.021266973}
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