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Simplifying (7a + -6b + -5c)(7a + -6b + -5c) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 Multiply (7a + -6b + -5c) * (7a + -6b + -5c) (7a * (7a + -6b + -5c) + -6b * (7a + -6b + -5c) + -5c * (7a + -6b + -5c)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 ((7a * 7a + -6b * 7a + -5c * 7a) + -6b * (7a + -6b + -5c) + -5c * (7a + -6b + -5c)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 Reorder the terms: ((-42ab + -35ac + 49a2) + -6b * (7a + -6b + -5c) + -5c * (7a + -6b + -5c)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 ((-42ab + -35ac + 49a2) + -6b * (7a + -6b + -5c) + -5c * (7a + -6b + -5c)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 (-42ab + -35ac + 49a2 + (7a * -6b + -6b * -6b + -5c * -6b) + -5c * (7a + -6b + -5c)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 Reorder the terms: (-42ab + -35ac + 49a2 + (-42ab + 30bc + 36b2) + -5c * (7a + -6b + -5c)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 (-42ab + -35ac + 49a2 + (-42ab + 30bc + 36b2) + -5c * (7a + -6b + -5c)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 (-42ab + -35ac + 49a2 + -42ab + 30bc + 36b2 + (7a * -5c + -6b * -5c + -5c * -5c)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 (-42ab + -35ac + 49a2 + -42ab + 30bc + 36b2 + (-35ac + 30bc + 25c2)) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 Reorder the terms: (-42ab + -42ab + -35ac + -35ac + 49a2 + 30bc + 30bc + 36b2 + 25c2) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 Combine like terms: -42ab + -42ab = -84ab (-84ab + -35ac + -35ac + 49a2 + 30bc + 30bc + 36b2 + 25c2) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 Combine like terms: -35ac + -35ac = -70ac (-84ab + -70ac + 49a2 + 30bc + 30bc + 36b2 + 25c2) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 Combine like terms: 30bc + 30bc = 60bc (-84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2) + (7a + 6b + -5c)(7a + 6b + -5c) = 0 Multiply (7a + 6b + -5c) * (7a + 6b + -5c) -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (7a * (7a + 6b + -5c) + 6b * (7a + 6b + -5c) + -5c * (7a + 6b + -5c)) = 0 -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + ((7a * 7a + 6b * 7a + -5c * 7a) + 6b * (7a + 6b + -5c) + -5c * (7a + 6b + -5c)) = 0 Reorder the terms: -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + ((42ab + -35ac + 49a2) + 6b * (7a + 6b + -5c) + -5c * (7a + 6b + -5c)) = 0 -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + ((42ab + -35ac + 49a2) + 6b * (7a + 6b + -5c) + -5c * (7a + 6b + -5c)) = 0 -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (42ab + -35ac + 49a2 + (7a * 6b + 6b * 6b + -5c * 6b) + -5c * (7a + 6b + -5c)) = 0 Reorder the terms: -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (42ab + -35ac + 49a2 + (42ab + -30bc + 36b2) + -5c * (7a + 6b + -5c)) = 0 -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (42ab + -35ac + 49a2 + (42ab + -30bc + 36b2) + -5c * (7a + 6b + -5c)) = 0 -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (42ab + -35ac + 49a2 + 42ab + -30bc + 36b2 + (7a * -5c + 6b * -5c + -5c * -5c)) = 0 -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (42ab + -35ac + 49a2 + 42ab + -30bc + 36b2 + (-35ac + -30bc + 25c2)) = 0 Reorder the terms: -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (42ab + 42ab + -35ac + -35ac + 49a2 + -30bc + -30bc + 36b2 + 25c2) = 0 Combine like terms: 42ab + 42ab = 84ab -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (84ab + -35ac + -35ac + 49a2 + -30bc + -30bc + 36b2 + 25c2) = 0 Combine like terms: -35ac + -35ac = -70ac -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (84ab + -70ac + 49a2 + -30bc + -30bc + 36b2 + 25c2) = 0 Combine like terms: -30bc + -30bc = -60bc -84ab + -70ac + 49a2 + 60bc + 36b2 + 25c2 + (84ab + -70ac + 49a2 + -60bc + 36b2 + 25c2) = 0 Reorder the terms: -84ab + 84ab + -70ac + -70ac + 49a2 + 49a2 + 60bc + -60bc + 36b2 + 36b2 + 25c2 + 25c2 = 0 Combine like terms: -84ab + 84ab = 0 0 + -70ac + -70ac + 49a2 + 49a2 + 60bc + -60bc + 36b2 + 36b2 + 25c2 + 25c2 = 0 -70ac + -70ac + 49a2 + 49a2 + 60bc + -60bc + 36b2 + 36b2 + 25c2 + 25c2 = 0 Combine like terms: -70ac + -70ac = -140ac -140ac + 49a2 + 49a2 + 60bc + -60bc + 36b2 + 36b2 + 25c2 + 25c2 = 0 Combine like terms: 49a2 + 49a2 = 98a2 -140ac + 98a2 + 60bc + -60bc + 36b2 + 36b2 + 25c2 + 25c2 = 0 Combine like terms: 60bc + -60bc = 0 -140ac + 98a2 + 0 + 36b2 + 36b2 + 25c2 + 25c2 = 0 -140ac + 98a2 + 36b2 + 36b2 + 25c2 + 25c2 = 0 Combine like terms: 36b2 + 36b2 = 72b2 -140ac + 98a2 + 72b2 + 25c2 + 25c2 = 0 Combine like terms: 25c2 + 25c2 = 50c2 -140ac + 98a2 + 72b2 + 50c2 = 0 Solving -140ac + 98a2 + 72b2 + 50c2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-70ac + 49a2 + 36b2 + 25c2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-70ac + 49a2 + 36b2 + 25c2)' equal to zero and attempt to solve: Simplifying -70ac + 49a2 + 36b2 + 25c2 = 0 Solving -70ac + 49a2 + 36b2 + 25c2 = 0 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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