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Simplifying x2 + -4x + -2069 = 0 Reorder the terms: -2069 + -4x + x2 = 0 Solving -2069 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2069' to each side of the equation. -2069 + -4x + 2069 + x2 = 0 + 2069 Reorder the terms: -2069 + 2069 + -4x + x2 = 0 + 2069 Combine like terms: -2069 + 2069 = 0 0 + -4x + x2 = 0 + 2069 -4x + x2 = 0 + 2069 Combine like terms: 0 + 2069 = 2069 -4x + x2 = 2069 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 = 2069 + 4 Reorder the terms: 4 + -4x + x2 = 2069 + 4 Combine like terms: 2069 + 4 = 2073 4 + -4x + x2 = 2073 Factor a perfect square on the left side: (x + -2)(x + -2) = 2073 Calculate the square root of the right side: 45.530209751 Break this problem into two subproblems by setting (x + -2) equal to 45.530209751 and -45.530209751.Subproblem 1
x + -2 = 45.530209751 Simplifying x + -2 = 45.530209751 Reorder the terms: -2 + x = 45.530209751 Solving -2 + x = 45.530209751 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 = 45.530209751 + 2 Combine like terms: -2 + 2 = 0 0 + x = 45.530209751 + 2 x = 45.530209751 + 2 Combine like terms: 45.530209751 + 2 = 47.530209751 x = 47.530209751 Simplifying x = 47.530209751Subproblem 2
x + -2 = -45.530209751 Simplifying x + -2 = -45.530209751 Reorder the terms: -2 + x = -45.530209751 Solving -2 + x = -45.530209751 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 = -45.530209751 + 2 Combine like terms: -2 + 2 = 0 0 + x = -45.530209751 + 2 x = -45.530209751 + 2 Combine like terms: -45.530209751 + 2 = -43.530209751 x = -43.530209751 Simplifying x = -43.530209751Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.530209751, -43.530209751}
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