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Simplifying x2 + -4x + 4 = 128 Reorder the terms: 4 + -4x + x2 = 128 Solving 4 + -4x + x2 = 128 Solving for variable 'x'. Reorder the terms: 4 + -128 + -4x + x2 = 128 + -128 Combine like terms: 4 + -128 = -124 -124 + -4x + x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -124 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '124' to each side of the equation. -124 + -4x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + -4x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + -4x + x2 = 0 + 124 -4x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 -4x + x2 = 124 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 = 124 + 4 Reorder the terms: 4 + -4x + x2 = 124 + 4 Combine like terms: 124 + 4 = 128 4 + -4x + x2 = 128 Factor a perfect square on the left side: (x + -2)(x + -2) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + -2) equal to 11.313708499 and -11.313708499.Subproblem 1
x + -2 = 11.313708499 Simplifying x + -2 = 11.313708499 Reorder the terms: -2 + x = 11.313708499 Solving -2 + x = 11.313708499 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 = 11.313708499 + 2 Combine like terms: -2 + 2 = 0 0 + x = 11.313708499 + 2 x = 11.313708499 + 2 Combine like terms: 11.313708499 + 2 = 13.313708499 x = 13.313708499 Simplifying x = 13.313708499Subproblem 2
x + -2 = -11.313708499 Simplifying x + -2 = -11.313708499 Reorder the terms: -2 + x = -11.313708499 Solving -2 + x = -11.313708499 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 = -11.313708499 + 2 Combine like terms: -2 + 2 = 0 0 + x = -11.313708499 + 2 x = -11.313708499 + 2 Combine like terms: -11.313708499 + 2 = -9.313708499 x = -9.313708499 Simplifying x = -9.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.313708499, -9.313708499}
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