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Simplifying 4x + 5 = x2 + 31x + 240 Reorder the terms: 5 + 4x = x2 + 31x + 240 Reorder the terms: 5 + 4x = 240 + 31x + x2 Solving 5 + 4x = 240 + 31x + x2 Solving for variable 'x'. Reorder the terms: 5 + -240 + 4x + -31x + -1x2 = 240 + 31x + x2 + -240 + -31x + -1x2 Combine like terms: 5 + -240 = -235 -235 + 4x + -31x + -1x2 = 240 + 31x + x2 + -240 + -31x + -1x2 Combine like terms: 4x + -31x = -27x -235 + -27x + -1x2 = 240 + 31x + x2 + -240 + -31x + -1x2 Reorder the terms: -235 + -27x + -1x2 = 240 + -240 + 31x + -31x + x2 + -1x2 Combine like terms: 240 + -240 = 0 -235 + -27x + -1x2 = 0 + 31x + -31x + x2 + -1x2 -235 + -27x + -1x2 = 31x + -31x + x2 + -1x2 Combine like terms: 31x + -31x = 0 -235 + -27x + -1x2 = 0 + x2 + -1x2 -235 + -27x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -235 + -27x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(235 + 27x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(235 + 27x + x2)' equal to zero and attempt to solve: Simplifying 235 + 27x + x2 = 0 Solving 235 + 27x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-235' to each side of the equation. 235 + 27x + -235 + x2 = 0 + -235 Reorder the terms: 235 + -235 + 27x + x2 = 0 + -235 Combine like terms: 235 + -235 = 0 0 + 27x + x2 = 0 + -235 27x + x2 = 0 + -235 Combine like terms: 0 + -235 = -235 27x + x2 = -235 The x term is 27x. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27x + 182.25 + x2 = -235 + 182.25 Reorder the terms: 182.25 + 27x + x2 = -235 + 182.25 Combine like terms: -235 + 182.25 = -52.75 182.25 + 27x + x2 = -52.75 Factor a perfect square on the left side: (x + 13.5)(x + 13.5) = -52.75 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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