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Simplifying x2 + 134x + -10000 = 0 Reorder the terms: -10000 + 134x + x2 = 0 Solving -10000 + 134x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 134x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 134x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 134x + x2 = 0 + 10000 134x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 134x + x2 = 10000 The x term is 134x. Take half its coefficient (67). Square it (4489) and add it to both sides. Add '4489' to each side of the equation. 134x + 4489 + x2 = 10000 + 4489 Reorder the terms: 4489 + 134x + x2 = 10000 + 4489 Combine like terms: 10000 + 4489 = 14489 4489 + 134x + x2 = 14489 Factor a perfect square on the left side: (x + 67)(x + 67) = 14489 Calculate the square root of the right side: 120.370262108 Break this problem into two subproblems by setting (x + 67) equal to 120.370262108 and -120.370262108.Subproblem 1
x + 67 = 120.370262108 Simplifying x + 67 = 120.370262108 Reorder the terms: 67 + x = 120.370262108 Solving 67 + x = 120.370262108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-67' to each side of the equation. 67 + -67 + x = 120.370262108 + -67 Combine like terms: 67 + -67 = 0 0 + x = 120.370262108 + -67 x = 120.370262108 + -67 Combine like terms: 120.370262108 + -67 = 53.370262108 x = 53.370262108 Simplifying x = 53.370262108Subproblem 2
x + 67 = -120.370262108 Simplifying x + 67 = -120.370262108 Reorder the terms: 67 + x = -120.370262108 Solving 67 + x = -120.370262108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-67' to each side of the equation. 67 + -67 + x = -120.370262108 + -67 Combine like terms: 67 + -67 = 0 0 + x = -120.370262108 + -67 x = -120.370262108 + -67 Combine like terms: -120.370262108 + -67 = -187.370262108 x = -187.370262108 Simplifying x = -187.370262108Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.370262108, -187.370262108}
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