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Simplifying x2 + -3x + 5 = 10543 Reorder the terms: 5 + -3x + x2 = 10543 Solving 5 + -3x + x2 = 10543 Solving for variable 'x'. Reorder the terms: 5 + -10543 + -3x + x2 = 10543 + -10543 Combine like terms: 5 + -10543 = -10538 -10538 + -3x + x2 = 10543 + -10543 Combine like terms: 10543 + -10543 = 0 -10538 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10538' to each side of the equation. -10538 + -3x + 10538 + x2 = 0 + 10538 Reorder the terms: -10538 + 10538 + -3x + x2 = 0 + 10538 Combine like terms: -10538 + 10538 = 0 0 + -3x + x2 = 0 + 10538 -3x + x2 = 0 + 10538 Combine like terms: 0 + 10538 = 10538 -3x + x2 = 10538 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 10538 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 10538 + 2.25 Combine like terms: 10538 + 2.25 = 10540.25 2.25 + -3x + x2 = 10540.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10540.25 Calculate the square root of the right side: 102.665719693 Break this problem into two subproblems by setting (x + -1.5) equal to 102.665719693 and -102.665719693.Subproblem 1
x + -1.5 = 102.665719693 Simplifying x + -1.5 = 102.665719693 Reorder the terms: -1.5 + x = 102.665719693 Solving -1.5 + x = 102.665719693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 102.665719693 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 102.665719693 + 1.5 x = 102.665719693 + 1.5 Combine like terms: 102.665719693 + 1.5 = 104.165719693 x = 104.165719693 Simplifying x = 104.165719693Subproblem 2
x + -1.5 = -102.665719693 Simplifying x + -1.5 = -102.665719693 Reorder the terms: -1.5 + x = -102.665719693 Solving -1.5 + x = -102.665719693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -102.665719693 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -102.665719693 + 1.5 x = -102.665719693 + 1.5 Combine like terms: -102.665719693 + 1.5 = -101.165719693 x = -101.165719693 Simplifying x = -101.165719693Solution
The solution to the problem is based on the solutions from the subproblems. x = {104.165719693, -101.165719693}
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