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Simplifying x2 + 1045x + 14278 = 0 Reorder the terms: 14278 + 1045x + x2 = 0 Solving 14278 + 1045x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14278' to each side of the equation. 14278 + 1045x + -14278 + x2 = 0 + -14278 Reorder the terms: 14278 + -14278 + 1045x + x2 = 0 + -14278 Combine like terms: 14278 + -14278 = 0 0 + 1045x + x2 = 0 + -14278 1045x + x2 = 0 + -14278 Combine like terms: 0 + -14278 = -14278 1045x + x2 = -14278 The x term is 1045x. Take half its coefficient (522.5). Square it (273006.25) and add it to both sides. Add '273006.25' to each side of the equation. 1045x + 273006.25 + x2 = -14278 + 273006.25 Reorder the terms: 273006.25 + 1045x + x2 = -14278 + 273006.25 Combine like terms: -14278 + 273006.25 = 258728.25 273006.25 + 1045x + x2 = 258728.25 Factor a perfect square on the left side: (x + 522.5)(x + 522.5) = 258728.25 Calculate the square root of the right side: 508.653369201 Break this problem into two subproblems by setting (x + 522.5) equal to 508.653369201 and -508.653369201.Subproblem 1
x + 522.5 = 508.653369201 Simplifying x + 522.5 = 508.653369201 Reorder the terms: 522.5 + x = 508.653369201 Solving 522.5 + x = 508.653369201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-522.5' to each side of the equation. 522.5 + -522.5 + x = 508.653369201 + -522.5 Combine like terms: 522.5 + -522.5 = 0.0 0.0 + x = 508.653369201 + -522.5 x = 508.653369201 + -522.5 Combine like terms: 508.653369201 + -522.5 = -13.846630799 x = -13.846630799 Simplifying x = -13.846630799Subproblem 2
x + 522.5 = -508.653369201 Simplifying x + 522.5 = -508.653369201 Reorder the terms: 522.5 + x = -508.653369201 Solving 522.5 + x = -508.653369201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-522.5' to each side of the equation. 522.5 + -522.5 + x = -508.653369201 + -522.5 Combine like terms: 522.5 + -522.5 = 0.0 0.0 + x = -508.653369201 + -522.5 x = -508.653369201 + -522.5 Combine like terms: -508.653369201 + -522.5 = -1031.153369201 x = -1031.153369201 Simplifying x = -1031.153369201Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.846630799, -1031.153369201}
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