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Simplifying x = x2 + 40x + 500 Reorder the terms: x = 500 + 40x + x2 Solving x = 500 + 40x + x2 Solving for variable 'x'. Reorder the terms: -500 + x + -40x + -1x2 = 500 + 40x + x2 + -500 + -40x + -1x2 Combine like terms: x + -40x = -39x -500 + -39x + -1x2 = 500 + 40x + x2 + -500 + -40x + -1x2 Reorder the terms: -500 + -39x + -1x2 = 500 + -500 + 40x + -40x + x2 + -1x2 Combine like terms: 500 + -500 = 0 -500 + -39x + -1x2 = 0 + 40x + -40x + x2 + -1x2 -500 + -39x + -1x2 = 40x + -40x + x2 + -1x2 Combine like terms: 40x + -40x = 0 -500 + -39x + -1x2 = 0 + x2 + -1x2 -500 + -39x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -500 + -39x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(500 + 39x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(500 + 39x + x2)' equal to zero and attempt to solve: Simplifying 500 + 39x + x2 = 0 Solving 500 + 39x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + 39x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + 39x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + 39x + x2 = 0 + -500 39x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 39x + x2 = -500 The x term is 39x. Take half its coefficient (19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. 39x + 380.25 + x2 = -500 + 380.25 Reorder the terms: 380.25 + 39x + x2 = -500 + 380.25 Combine like terms: -500 + 380.25 = -119.75 380.25 + 39x + x2 = -119.75 Factor a perfect square on the left side: (x + 19.5)(x + 19.5) = -119.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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