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Simplifying x2 + -8x + -10008 = 0 Reorder the terms: -10008 + -8x + x2 = 0 Solving -10008 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10008' to each side of the equation. -10008 + -8x + 10008 + x2 = 0 + 10008 Reorder the terms: -10008 + 10008 + -8x + x2 = 0 + 10008 Combine like terms: -10008 + 10008 = 0 0 + -8x + x2 = 0 + 10008 -8x + x2 = 0 + 10008 Combine like terms: 0 + 10008 = 10008 -8x + x2 = 10008 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 10008 + 16 Reorder the terms: 16 + -8x + x2 = 10008 + 16 Combine like terms: 10008 + 16 = 10024 16 + -8x + x2 = 10024 Factor a perfect square on the left side: (x + -4)(x + -4) = 10024 Calculate the square root of the right side: 100.119928086 Break this problem into two subproblems by setting (x + -4) equal to 100.119928086 and -100.119928086.Subproblem 1
x + -4 = 100.119928086 Simplifying x + -4 = 100.119928086 Reorder the terms: -4 + x = 100.119928086 Solving -4 + x = 100.119928086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 100.119928086 + 4 Combine like terms: -4 + 4 = 0 0 + x = 100.119928086 + 4 x = 100.119928086 + 4 Combine like terms: 100.119928086 + 4 = 104.119928086 x = 104.119928086 Simplifying x = 104.119928086Subproblem 2
x + -4 = -100.119928086 Simplifying x + -4 = -100.119928086 Reorder the terms: -4 + x = -100.119928086 Solving -4 + x = -100.119928086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -100.119928086 + 4 Combine like terms: -4 + 4 = 0 0 + x = -100.119928086 + 4 x = -100.119928086 + 4 Combine like terms: -100.119928086 + 4 = -96.119928086 x = -96.119928086 Simplifying x = -96.119928086Solution
The solution to the problem is based on the solutions from the subproblems. x = {104.119928086, -96.119928086}
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