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Simplifying x2 + -2x + -535 = 0 Reorder the terms: -535 + -2x + x2 = 0 Solving -535 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '535' to each side of the equation. -535 + -2x + 535 + x2 = 0 + 535 Reorder the terms: -535 + 535 + -2x + x2 = 0 + 535 Combine like terms: -535 + 535 = 0 0 + -2x + x2 = 0 + 535 -2x + x2 = 0 + 535 Combine like terms: 0 + 535 = 535 -2x + x2 = 535 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 535 + 1 Reorder the terms: 1 + -2x + x2 = 535 + 1 Combine like terms: 535 + 1 = 536 1 + -2x + x2 = 536 Factor a perfect square on the left side: (x + -1)(x + -1) = 536 Calculate the square root of the right side: 23.151673806 Break this problem into two subproblems by setting (x + -1) equal to 23.151673806 and -23.151673806.Subproblem 1
x + -1 = 23.151673806 Simplifying x + -1 = 23.151673806 Reorder the terms: -1 + x = 23.151673806 Solving -1 + x = 23.151673806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 23.151673806 + 1 Combine like terms: -1 + 1 = 0 0 + x = 23.151673806 + 1 x = 23.151673806 + 1 Combine like terms: 23.151673806 + 1 = 24.151673806 x = 24.151673806 Simplifying x = 24.151673806Subproblem 2
x + -1 = -23.151673806 Simplifying x + -1 = -23.151673806 Reorder the terms: -1 + x = -23.151673806 Solving -1 + x = -23.151673806 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -23.151673806 + 1 Combine like terms: -1 + 1 = 0 0 + x = -23.151673806 + 1 x = -23.151673806 + 1 Combine like terms: -23.151673806 + 1 = -22.151673806 x = -22.151673806 Simplifying x = -22.151673806Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.151673806, -22.151673806}
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