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Simplifying x2 + 2x + -523 = 0 Reorder the terms: -523 + 2x + x2 = 0 Solving -523 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '523' to each side of the equation. -523 + 2x + 523 + x2 = 0 + 523 Reorder the terms: -523 + 523 + 2x + x2 = 0 + 523 Combine like terms: -523 + 523 = 0 0 + 2x + x2 = 0 + 523 2x + x2 = 0 + 523 Combine like terms: 0 + 523 = 523 2x + x2 = 523 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 = 523 + 1 Reorder the terms: 1 + 2x + x2 = 523 + 1 Combine like terms: 523 + 1 = 524 1 + 2x + x2 = 524 Factor a perfect square on the left side: (x + 1)(x + 1) = 524 Calculate the square root of the right side: 22.891046285 Break this problem into two subproblems by setting (x + 1) equal to 22.891046285 and -22.891046285.Subproblem 1
x + 1 = 22.891046285 Simplifying x + 1 = 22.891046285 Reorder the terms: 1 + x = 22.891046285 Solving 1 + x = 22.891046285 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 = 22.891046285 + -1 Combine like terms: 1 + -1 = 0 0 + x = 22.891046285 + -1 x = 22.891046285 + -1 Combine like terms: 22.891046285 + -1 = 21.891046285 x = 21.891046285 Simplifying x = 21.891046285Subproblem 2
x + 1 = -22.891046285 Simplifying x + 1 = -22.891046285 Reorder the terms: 1 + x = -22.891046285 Solving 1 + x = -22.891046285 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 = -22.891046285 + -1 Combine like terms: 1 + -1 = 0 0 + x = -22.891046285 + -1 x = -22.891046285 + -1 Combine like terms: -22.891046285 + -1 = -23.891046285 x = -23.891046285 Simplifying x = -23.891046285Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.891046285, -23.891046285}
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