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Simplifying (x) = x2 + 18x + 77 x = x2 + 18x + 77 Reorder the terms: x = 77 + 18x + x2 Solving x = 77 + 18x + x2 Solving for variable 'x'. Reorder the terms: -77 + x + -18x + -1x2 = 77 + 18x + x2 + -77 + -18x + -1x2 Combine like terms: x + -18x = -17x -77 + -17x + -1x2 = 77 + 18x + x2 + -77 + -18x + -1x2 Reorder the terms: -77 + -17x + -1x2 = 77 + -77 + 18x + -18x + x2 + -1x2 Combine like terms: 77 + -77 = 0 -77 + -17x + -1x2 = 0 + 18x + -18x + x2 + -1x2 -77 + -17x + -1x2 = 18x + -18x + x2 + -1x2 Combine like terms: 18x + -18x = 0 -77 + -17x + -1x2 = 0 + x2 + -1x2 -77 + -17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -77 + -17x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(77 + 17x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(77 + 17x + x2)' equal to zero and attempt to solve: Simplifying 77 + 17x + x2 = 0 Solving 77 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-77' to each side of the equation. 77 + 17x + -77 + x2 = 0 + -77 Reorder the terms: 77 + -77 + 17x + x2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + 17x + x2 = 0 + -77 17x + x2 = 0 + -77 Combine like terms: 0 + -77 = -77 17x + x2 = -77 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -77 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -77 + 72.25 Combine like terms: -77 + 72.25 = -4.75 72.25 + 17x + x2 = -4.75 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = -4.75 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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