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Simplifying x2 + -2x + -130 = 0 Reorder the terms: -130 + -2x + x2 = 0 Solving -130 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + -2x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + -2x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -2x + x2 = 0 + 130 -2x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 -2x + x2 = 130 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 = 130 + 1 Reorder the terms: 1 + -2x + x2 = 130 + 1 Combine like terms: 130 + 1 = 131 1 + -2x + x2 = 131 Factor a perfect square on the left side: (x + -1)(x + -1) = 131 Calculate the square root of the right side: 11.445523142 Break this problem into two subproblems by setting (x + -1) equal to 11.445523142 and -11.445523142.Subproblem 1
x + -1 = 11.445523142 Simplifying x + -1 = 11.445523142 Reorder the terms: -1 + x = 11.445523142 Solving -1 + x = 11.445523142 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 = 11.445523142 + 1 Combine like terms: -1 + 1 = 0 0 + x = 11.445523142 + 1 x = 11.445523142 + 1 Combine like terms: 11.445523142 + 1 = 12.445523142 x = 12.445523142 Simplifying x = 12.445523142Subproblem 2
x + -1 = -11.445523142 Simplifying x + -1 = -11.445523142 Reorder the terms: -1 + x = -11.445523142 Solving -1 + x = -11.445523142 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 = -11.445523142 + 1 Combine like terms: -1 + 1 = 0 0 + x = -11.445523142 + 1 x = -11.445523142 + 1 Combine like terms: -11.445523142 + 1 = -10.445523142 x = -10.445523142 Simplifying x = -10.445523142Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.445523142, -10.445523142}
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