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Simplifying x2 + 4x + -123 = 1000 Reorder the terms: -123 + 4x + x2 = 1000 Solving -123 + 4x + x2 = 1000 Solving for variable 'x'. Reorder the terms: -123 + -1000 + 4x + x2 = 1000 + -1000 Combine like terms: -123 + -1000 = -1123 -1123 + 4x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1123 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1123' to each side of the equation. -1123 + 4x + 1123 + x2 = 0 + 1123 Reorder the terms: -1123 + 1123 + 4x + x2 = 0 + 1123 Combine like terms: -1123 + 1123 = 0 0 + 4x + x2 = 0 + 1123 4x + x2 = 0 + 1123 Combine like terms: 0 + 1123 = 1123 4x + x2 = 1123 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1123 + 4 Reorder the terms: 4 + 4x + x2 = 1123 + 4 Combine like terms: 1123 + 4 = 1127 4 + 4x + x2 = 1127 Factor a perfect square on the left side: (x + 2)(x + 2) = 1127 Calculate the square root of the right side: 33.570820663 Break this problem into two subproblems by setting (x + 2) equal to 33.570820663 and -33.570820663.Subproblem 1
x + 2 = 33.570820663 Simplifying x + 2 = 33.570820663 Reorder the terms: 2 + x = 33.570820663 Solving 2 + x = 33.570820663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 33.570820663 + -2 Combine like terms: 2 + -2 = 0 0 + x = 33.570820663 + -2 x = 33.570820663 + -2 Combine like terms: 33.570820663 + -2 = 31.570820663 x = 31.570820663 Simplifying x = 31.570820663Subproblem 2
x + 2 = -33.570820663 Simplifying x + 2 = -33.570820663 Reorder the terms: 2 + x = -33.570820663 Solving 2 + x = -33.570820663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -33.570820663 + -2 Combine like terms: 2 + -2 = 0 0 + x = -33.570820663 + -2 x = -33.570820663 + -2 Combine like terms: -33.570820663 + -2 = -35.570820663 x = -35.570820663 Simplifying x = -35.570820663Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.570820663, -35.570820663}
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