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Simplifying x2 + -4x + 4 = 1000 Reorder the terms: 4 + -4x + x2 = 1000 Solving 4 + -4x + x2 = 1000 Solving for variable 'x'. Reorder the terms: 4 + -1000 + -4x + x2 = 1000 + -1000 Combine like terms: 4 + -1000 = -996 -996 + -4x + x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -996 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '996' to each side of the equation. -996 + -4x + 996 + x2 = 0 + 996 Reorder the terms: -996 + 996 + -4x + x2 = 0 + 996 Combine like terms: -996 + 996 = 0 0 + -4x + x2 = 0 + 996 -4x + x2 = 0 + 996 Combine like terms: 0 + 996 = 996 -4x + x2 = 996 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 = 996 + 4 Reorder the terms: 4 + -4x + x2 = 996 + 4 Combine like terms: 996 + 4 = 1000 4 + -4x + x2 = 1000 Factor a perfect square on the left side: (x + -2)(x + -2) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + -2) equal to 31.622776602 and -31.622776602.Subproblem 1
x + -2 = 31.622776602 Simplifying x + -2 = 31.622776602 Reorder the terms: -2 + x = 31.622776602 Solving -2 + x = 31.622776602 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 = 31.622776602 + 2 Combine like terms: -2 + 2 = 0 0 + x = 31.622776602 + 2 x = 31.622776602 + 2 Combine like terms: 31.622776602 + 2 = 33.622776602 x = 33.622776602 Simplifying x = 33.622776602Subproblem 2
x + -2 = -31.622776602 Simplifying x + -2 = -31.622776602 Reorder the terms: -2 + x = -31.622776602 Solving -2 + x = -31.622776602 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 = -31.622776602 + 2 Combine like terms: -2 + 2 = 0 0 + x = -31.622776602 + 2 x = -31.622776602 + 2 Combine like terms: -31.622776602 + 2 = -29.622776602 x = -29.622776602 Simplifying x = -29.622776602Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.622776602, -29.622776602}
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