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Simplifying x2 + -2x + -488 = 0 Reorder the terms: -488 + -2x + x2 = 0 Solving -488 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '488' to each side of the equation. -488 + -2x + 488 + x2 = 0 + 488 Reorder the terms: -488 + 488 + -2x + x2 = 0 + 488 Combine like terms: -488 + 488 = 0 0 + -2x + x2 = 0 + 488 -2x + x2 = 0 + 488 Combine like terms: 0 + 488 = 488 -2x + x2 = 488 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 = 488 + 1 Reorder the terms: 1 + -2x + x2 = 488 + 1 Combine like terms: 488 + 1 = 489 1 + -2x + x2 = 489 Factor a perfect square on the left side: (x + -1)(x + -1) = 489 Calculate the square root of the right side: 22.113344387 Break this problem into two subproblems by setting (x + -1) equal to 22.113344387 and -22.113344387.Subproblem 1
x + -1 = 22.113344387 Simplifying x + -1 = 22.113344387 Reorder the terms: -1 + x = 22.113344387 Solving -1 + x = 22.113344387 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 = 22.113344387 + 1 Combine like terms: -1 + 1 = 0 0 + x = 22.113344387 + 1 x = 22.113344387 + 1 Combine like terms: 22.113344387 + 1 = 23.113344387 x = 23.113344387 Simplifying x = 23.113344387Subproblem 2
x + -1 = -22.113344387 Simplifying x + -1 = -22.113344387 Reorder the terms: -1 + x = -22.113344387 Solving -1 + x = -22.113344387 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 = -22.113344387 + 1 Combine like terms: -1 + 1 = 0 0 + x = -22.113344387 + 1 x = -22.113344387 + 1 Combine like terms: -22.113344387 + 1 = -21.113344387 x = -21.113344387 Simplifying x = -21.113344387Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.113344387, -21.113344387}
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