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Simplifying 2x + 1 = x2 + 18x + 81 Reorder the terms: 1 + 2x = x2 + 18x + 81 Reorder the terms: 1 + 2x = 81 + 18x + x2 Solving 1 + 2x = 81 + 18x + x2 Solving for variable 'x'. Reorder the terms: 1 + -81 + 2x + -18x + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2 Combine like terms: 1 + -81 = -80 -80 + 2x + -18x + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2 Combine like terms: 2x + -18x = -16x -80 + -16x + -1x2 = 81 + 18x + x2 + -81 + -18x + -1x2 Reorder the terms: -80 + -16x + -1x2 = 81 + -81 + 18x + -18x + x2 + -1x2 Combine like terms: 81 + -81 = 0 -80 + -16x + -1x2 = 0 + 18x + -18x + x2 + -1x2 -80 + -16x + -1x2 = 18x + -18x + x2 + -1x2 Combine like terms: 18x + -18x = 0 -80 + -16x + -1x2 = 0 + x2 + -1x2 -80 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -80 + -16x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(80 + 16x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(80 + 16x + x2)' equal to zero and attempt to solve: Simplifying 80 + 16x + x2 = 0 Solving 80 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 16x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + 16x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 16x + x2 = 0 + -80 16x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 16x + x2 = -80 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -80 + 64 Reorder the terms: 64 + 16x + x2 = -80 + 64 Combine like terms: -80 + 64 = -16 64 + 16x + x2 = -16 Factor a perfect square on the left side: (x + 8)(x + 8) = -16 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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