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Simplifying x2 + 1807x + -4200 = 0 Reorder the terms: -4200 + 1807x + x2 = 0 Solving -4200 + 1807x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4200' to each side of the equation. -4200 + 1807x + 4200 + x2 = 0 + 4200 Reorder the terms: -4200 + 4200 + 1807x + x2 = 0 + 4200 Combine like terms: -4200 + 4200 = 0 0 + 1807x + x2 = 0 + 4200 1807x + x2 = 0 + 4200 Combine like terms: 0 + 4200 = 4200 1807x + x2 = 4200 The x term is 1807x. Take half its coefficient (903.5). Square it (816312.25) and add it to both sides. Add '816312.25' to each side of the equation. 1807x + 816312.25 + x2 = 4200 + 816312.25 Reorder the terms: 816312.25 + 1807x + x2 = 4200 + 816312.25 Combine like terms: 4200 + 816312.25 = 820512.25 816312.25 + 1807x + x2 = 820512.25 Factor a perfect square on the left side: (x + 903.5)(x + 903.5) = 820512.25 Calculate the square root of the right side: 905.821312401 Break this problem into two subproblems by setting (x + 903.5) equal to 905.821312401 and -905.821312401.Subproblem 1
x + 903.5 = 905.821312401 Simplifying x + 903.5 = 905.821312401 Reorder the terms: 903.5 + x = 905.821312401 Solving 903.5 + x = 905.821312401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-903.5' to each side of the equation. 903.5 + -903.5 + x = 905.821312401 + -903.5 Combine like terms: 903.5 + -903.5 = 0.0 0.0 + x = 905.821312401 + -903.5 x = 905.821312401 + -903.5 Combine like terms: 905.821312401 + -903.5 = 2.321312401 x = 2.321312401 Simplifying x = 2.321312401Subproblem 2
x + 903.5 = -905.821312401 Simplifying x + 903.5 = -905.821312401 Reorder the terms: 903.5 + x = -905.821312401 Solving 903.5 + x = -905.821312401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-903.5' to each side of the equation. 903.5 + -903.5 + x = -905.821312401 + -903.5 Combine like terms: 903.5 + -903.5 = 0.0 0.0 + x = -905.821312401 + -903.5 x = -905.821312401 + -903.5 Combine like terms: -905.821312401 + -903.5 = -1809.321312401 x = -1809.321312401 Simplifying x = -1809.321312401Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.321312401, -1809.321312401}
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