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Simplifying x2 + -6x + -130 = 0 Reorder the terms: -130 + -6x + x2 = 0 Solving -130 + -6x + 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 + -6x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + -6x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -6x + x2 = 0 + 130 -6x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 -6x + x2 = 130 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 130 + 9 Reorder the terms: 9 + -6x + x2 = 130 + 9 Combine like terms: 130 + 9 = 139 9 + -6x + x2 = 139 Factor a perfect square on the left side: (x + -3)(x + -3) = 139 Calculate the square root of the right side: 11.789826123 Break this problem into two subproblems by setting (x + -3) equal to 11.789826123 and -11.789826123.Subproblem 1
x + -3 = 11.789826123 Simplifying x + -3 = 11.789826123 Reorder the terms: -3 + x = 11.789826123 Solving -3 + x = 11.789826123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 11.789826123 + 3 Combine like terms: -3 + 3 = 0 0 + x = 11.789826123 + 3 x = 11.789826123 + 3 Combine like terms: 11.789826123 + 3 = 14.789826123 x = 14.789826123 Simplifying x = 14.789826123Subproblem 2
x + -3 = -11.789826123 Simplifying x + -3 = -11.789826123 Reorder the terms: -3 + x = -11.789826123 Solving -3 + x = -11.789826123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -11.789826123 + 3 Combine like terms: -3 + 3 = 0 0 + x = -11.789826123 + 3 x = -11.789826123 + 3 Combine like terms: -11.789826123 + 3 = -8.789826123 x = -8.789826123 Simplifying x = -8.789826123Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.789826123, -8.789826123}
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