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Simplifying x2 + -20x + -533 = 0 Reorder the terms: -533 + -20x + x2 = 0 Solving -533 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '533' to each side of the equation. -533 + -20x + 533 + x2 = 0 + 533 Reorder the terms: -533 + 533 + -20x + x2 = 0 + 533 Combine like terms: -533 + 533 = 0 0 + -20x + x2 = 0 + 533 -20x + x2 = 0 + 533 Combine like terms: 0 + 533 = 533 -20x + x2 = 533 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 533 + 100 Reorder the terms: 100 + -20x + x2 = 533 + 100 Combine like terms: 533 + 100 = 633 100 + -20x + x2 = 633 Factor a perfect square on the left side: (x + -10)(x + -10) = 633 Calculate the square root of the right side: 25.159491251 Break this problem into two subproblems by setting (x + -10) equal to 25.159491251 and -25.159491251.Subproblem 1
x + -10 = 25.159491251 Simplifying x + -10 = 25.159491251 Reorder the terms: -10 + x = 25.159491251 Solving -10 + x = 25.159491251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 25.159491251 + 10 Combine like terms: -10 + 10 = 0 0 + x = 25.159491251 + 10 x = 25.159491251 + 10 Combine like terms: 25.159491251 + 10 = 35.159491251 x = 35.159491251 Simplifying x = 35.159491251Subproblem 2
x + -10 = -25.159491251 Simplifying x + -10 = -25.159491251 Reorder the terms: -10 + x = -25.159491251 Solving -10 + x = -25.159491251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -25.159491251 + 10 Combine like terms: -10 + 10 = 0 0 + x = -25.159491251 + 10 x = -25.159491251 + 10 Combine like terms: -25.159491251 + 10 = -15.159491251 x = -15.159491251 Simplifying x = -15.159491251Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.159491251, -15.159491251}
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