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Simplifying x2 + -4x + -130 = 0 Reorder the terms: -130 + -4x + x2 = 0 Solving -130 + -4x + 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 + -4x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + -4x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -4x + x2 = 0 + 130 -4x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 -4x + x2 = 130 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 130 + 4 Reorder the terms: 4 + -4x + x2 = 130 + 4 Combine like terms: 130 + 4 = 134 4 + -4x + x2 = 134 Factor a perfect square on the left side: (x + -2)(x + -2) = 134 Calculate the square root of the right side: 11.575836903 Break this problem into two subproblems by setting (x + -2) equal to 11.575836903 and -11.575836903.Subproblem 1
x + -2 = 11.575836903 Simplifying x + -2 = 11.575836903 Reorder the terms: -2 + x = 11.575836903 Solving -2 + x = 11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 11.575836903 + 2 Combine like terms: -2 + 2 = 0 0 + x = 11.575836903 + 2 x = 11.575836903 + 2 Combine like terms: 11.575836903 + 2 = 13.575836903 x = 13.575836903 Simplifying x = 13.575836903Subproblem 2
x + -2 = -11.575836903 Simplifying x + -2 = -11.575836903 Reorder the terms: -2 + x = -11.575836903 Solving -2 + x = -11.575836903 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -11.575836903 + 2 Combine like terms: -2 + 2 = 0 0 + x = -11.575836903 + 2 x = -11.575836903 + 2 Combine like terms: -11.575836903 + 2 = -9.575836903 x = -9.575836903 Simplifying x = -9.575836903Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.575836903, -9.575836903}
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