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Simplifying (5sin2x + 4cosx + -4) * ln(x + -7) = 0 Reorder the terms: (-4 + 4cosx + 5in2sx) * ln(x + -7) = 0 Reorder the terms: (-4 + 4cosx + 5in2sx) * ln(-7 + x) = 0 Reorder the terms for easier multiplication: ln(-4 + 4cosx + 5in2sx)(-7 + x) = 0 Multiply (-4 + 4cosx + 5in2sx) * (-7 + x) ln(-4(-7 + x) + 4cosx * (-7 + x) + 5in2sx * (-7 + x)) = 0 ln((-7 * -4 + x * -4) + 4cosx * (-7 + x) + 5in2sx * (-7 + x)) = 0 ln((28 + -4x) + 4cosx * (-7 + x) + 5in2sx * (-7 + x)) = 0 ln(28 + -4x + (-7 * 4cosx + x * 4cosx) + 5in2sx * (-7 + x)) = 0 ln(28 + -4x + (-28cosx + 4cosx2) + 5in2sx * (-7 + x)) = 0 ln(28 + -4x + -28cosx + 4cosx2 + (-7 * 5in2sx + x * 5in2sx)) = 0 ln(28 + -4x + -28cosx + 4cosx2 + (-35in2sx + 5in2sx2)) = 0 Reorder the terms: ln(28 + -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -4x) = 0 ln(28 + -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -4x) = 0 (28 * ln + -28cosx * ln + 4cosx2 * ln + -35in2sx * ln + 5in2sx2 * ln + -4x * ln) = 0 Reorder the terms: (-28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx) = 0 (-28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx) = 0 Solving -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '35iln3sx' to each side of the equation. -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + 35iln3sx + -4lnx = 0 + 35iln3sx Reorder the terms: -28clnosx + 4clnosx2 + -35iln3sx + 35iln3sx + 5iln3sx2 + 28ln + -4lnx = 0 + 35iln3sx Combine like terms: -35iln3sx + 35iln3sx = 0 -28clnosx + 4clnosx2 + 0 + 5iln3sx2 + 28ln + -4lnx = 0 + 35iln3sx -28clnosx + 4clnosx2 + 5iln3sx2 + 28ln + -4lnx = 0 + 35iln3sx Remove the zero: -28clnosx + 4clnosx2 + 5iln3sx2 + 28ln + -4lnx = 35iln3sx Add '-5iln3sx2' to each side of the equation. -28clnosx + 4clnosx2 + 5iln3sx2 + 28ln + -5iln3sx2 + -4lnx = 35iln3sx + -5iln3sx2 Reorder the terms: -28clnosx + 4clnosx2 + 5iln3sx2 + -5iln3sx2 + 28ln + -4lnx = 35iln3sx + -5iln3sx2 Combine like terms: 5iln3sx2 + -5iln3sx2 = 0 -28clnosx + 4clnosx2 + 0 + 28ln + -4lnx = 35iln3sx + -5iln3sx2 -28clnosx + 4clnosx2 + 28ln + -4lnx = 35iln3sx + -5iln3sx2 Add '-28ln' to each side of the equation. -28clnosx + 4clnosx2 + 28ln + -28ln + -4lnx = 35iln3sx + -5iln3sx2 + -28ln Combine like terms: 28ln + -28ln = 0 -28clnosx + 4clnosx2 + 0 + -4lnx = 35iln3sx + -5iln3sx2 + -28ln -28clnosx + 4clnosx2 + -4lnx = 35iln3sx + -5iln3sx2 + -28ln Add '4lnx' to each side of the equation. -28clnosx + 4clnosx2 + -4lnx + 4lnx = 35iln3sx + -5iln3sx2 + -28ln + 4lnx Combine like terms: -4lnx + 4lnx = 0 -28clnosx + 4clnosx2 + 0 = 35iln3sx + -5iln3sx2 + -28ln + 4lnx -28clnosx + 4clnosx2 = 35iln3sx + -5iln3sx2 + -28ln + 4lnx Reorder the terms: -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = 35iln3sx + -35iln3sx + -5iln3sx2 + 5iln3sx2 + -28ln + 28ln + 4lnx + -4lnx Combine like terms: 35iln3sx + -35iln3sx = 0 -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = 0 + -5iln3sx2 + 5iln3sx2 + -28ln + 28ln + 4lnx + -4lnx -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = -5iln3sx2 + 5iln3sx2 + -28ln + 28ln + 4lnx + -4lnx Combine like terms: -5iln3sx2 + 5iln3sx2 = 0 -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = 0 + -28ln + 28ln + 4lnx + -4lnx -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = -28ln + 28ln + 4lnx + -4lnx Combine like terms: -28ln + 28ln = 0 -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = 0 + 4lnx + -4lnx -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = 4lnx + -4lnx Combine like terms: 4lnx + -4lnx = 0 -28clnosx + 4clnosx2 + -35iln3sx + 5iln3sx2 + 28ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(-28cosx + 4cosx2 + -35in2sx + 5in2sx2 + 28 + -4x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing c to the left, all other terms to the right. Add '-1ln' to each side of the equation. ln + -1ln = 0 + -1ln Remove the zero: 0 = -1ln Simplifying 0 = -1ln The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-28cosx + 4cosx2 + -35in2sx + 5in2sx2 + 28 + -4x)' equal to zero and attempt to solve: Simplifying -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + 28 + -4x = 0 Reorder the terms: 28 + -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -4x = 0 Solving 28 + -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -4x = 0 Move all terms containing c to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -28 + -4x = 0 + -28 Reorder the terms: 28 + -28 + -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -4x = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -4x = 0 + -28 -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -4x = 0 + -28 Combine like terms: 0 + -28 = -28 -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + -4x = -28 Add '35in2sx' to each side of the equation. -28cosx + 4cosx2 + -35in2sx + 5in2sx2 + 35in2sx + -4x = -28 + 35in2sx Reorder the terms: -28cosx + 4cosx2 + -35in2sx + 35in2sx + 5in2sx2 + -4x = -28 + 35in2sx Combine like terms: -35in2sx + 35in2sx = 0 -28cosx + 4cosx2 + 0 + 5in2sx2 + -4x = -28 + 35in2sx -28cosx + 4cosx2 + 5in2sx2 + -4x = -28 + 35in2sx Add '-5in2sx2' to each side of the equation. -28cosx + 4cosx2 + 5in2sx2 + -5in2sx2 + -4x = -28 + 35in2sx + -5in2sx2 Combine like terms: 5in2sx2 + -5in2sx2 = 0 -28cosx + 4cosx2 + 0 + -4x = -28 + 35in2sx + -5in2sx2 -28cosx + 4cosx2 + -4x = -28 + 35in2sx + -5in2sx2 Add '4x' to each side of the equation. -28cosx + 4cosx2 + -4x + 4x = -28 + 35in2sx + -5in2sx2 + 4x Combine like terms: -4x + 4x = 0 -28cosx + 4cosx2 + 0 = -28 + 35in2sx + -5in2sx2 + 4x -28cosx + 4cosx2 = -28 + 35in2sx + -5in2sx2 + 4x 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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