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Simplifying 0 = 150 + -5x + -1x2 + 117 Reorder the terms: 0 = 150 + 117 + -5x + -1x2 Combine like terms: 150 + 117 = 267 0 = 267 + -5x + -1x2 Solving 0 = 267 + -5x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -267 = -267 -267 + 5x + x2 = 267 + -5x + -1x2 + -267 + 5x + x2 Reorder the terms: -267 + 5x + x2 = 267 + -267 + -5x + 5x + -1x2 + x2 Combine like terms: 267 + -267 = 0 -267 + 5x + x2 = 0 + -5x + 5x + -1x2 + x2 -267 + 5x + x2 = -5x + 5x + -1x2 + x2 Combine like terms: -5x + 5x = 0 -267 + 5x + x2 = 0 + -1x2 + x2 -267 + 5x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -267 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '267' to each side of the equation. -267 + 5x + 267 + x2 = 0 + 267 Reorder the terms: -267 + 267 + 5x + x2 = 0 + 267 Combine like terms: -267 + 267 = 0 0 + 5x + x2 = 0 + 267 5x + x2 = 0 + 267 Combine like terms: 0 + 267 = 267 5x + x2 = 267 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 267 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 267 + 6.25 Combine like terms: 267 + 6.25 = 273.25 6.25 + 5x + x2 = 273.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 273.25 Calculate the square root of the right side: 16.530275255 Break this problem into two subproblems by setting (x + 2.5) equal to 16.530275255 and -16.530275255.Subproblem 1
x + 2.5 = 16.530275255 Simplifying x + 2.5 = 16.530275255 Reorder the terms: 2.5 + x = 16.530275255 Solving 2.5 + x = 16.530275255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 16.530275255 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 16.530275255 + -2.5 x = 16.530275255 + -2.5 Combine like terms: 16.530275255 + -2.5 = 14.030275255 x = 14.030275255 Simplifying x = 14.030275255Subproblem 2
x + 2.5 = -16.530275255 Simplifying x + 2.5 = -16.530275255 Reorder the terms: 2.5 + x = -16.530275255 Solving 2.5 + x = -16.530275255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -16.530275255 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -16.530275255 + -2.5 x = -16.530275255 + -2.5 Combine like terms: -16.530275255 + -2.5 = -19.030275255 x = -19.030275255 Simplifying x = -19.030275255Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.030275255, -19.030275255}
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