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Simplifying (10a + b)(10a + c) = 100a(a + 1) + bc Multiply (10a + b) * (10a + c) (10a * (10a + c) + b(10a + c)) = 100a(a + 1) + bc ((10a * 10a + c * 10a) + b(10a + c)) = 100a(a + 1) + bc Reorder the terms: ((10ac + 100a2) + b(10a + c)) = 100a(a + 1) + bc ((10ac + 100a2) + b(10a + c)) = 100a(a + 1) + bc (10ac + 100a2 + (10a * b + c * b)) = 100a(a + 1) + bc (10ac + 100a2 + (10ab + bc)) = 100a(a + 1) + bc Reorder the terms: (10ab + 10ac + 100a2 + bc) = 100a(a + 1) + bc (10ab + 10ac + 100a2 + bc) = 100a(a + 1) + bc Reorder the terms: 10ab + 10ac + 100a2 + bc = 100a(1 + a) + bc 10ab + 10ac + 100a2 + bc = (1 * 100a + a * 100a) + bc 10ab + 10ac + 100a2 + bc = (100a + 100a2) + bc Add '-100a2' to each side of the equation. 10ab + 10ac + 100a2 + -100a2 + bc = 100a + 100a2 + -100a2 + bc Combine like terms: 100a2 + -100a2 = 0 10ab + 10ac + 0 + bc = 100a + 100a2 + -100a2 + bc 10ab + 10ac + bc = 100a + 100a2 + -100a2 + bc Combine like terms: 100a2 + -100a2 = 0 10ab + 10ac + bc = 100a + 0 + bc 10ab + 10ac + bc = 100a + bc Add '-1bc' to each side of the equation. 10ab + 10ac + bc + -1bc = 100a + bc + -1bc Combine like terms: bc + -1bc = 0 10ab + 10ac + 0 = 100a + bc + -1bc 10ab + 10ac = 100a + bc + -1bc Combine like terms: bc + -1bc = 0 10ab + 10ac = 100a + 0 10ab + 10ac = 100a Solving 10ab + 10ac = 100a Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-100a' to each side of the equation. 10ab + -100a + 10ac = 100a + -100a Reorder the terms: -100a + 10ab + 10ac = 100a + -100a Combine like terms: 100a + -100a = 0 -100a + 10ab + 10ac = 0 Factor out the Greatest Common Factor (GCF), '10a'. 10a(-10 + b + c) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(-10 + b + c)' equal to zero and attempt to solve: Simplifying -10 + b + c = 0 Solving -10 + b + c = 0 Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + b + 10 + c = 0 + 10 Reorder the terms: -10 + 10 + b + c = 0 + 10 Combine like terms: -10 + 10 = 0 0 + b + c = 0 + 10 b + c = 0 + 10 Combine like terms: 0 + 10 = 10 b + c = 10 Add '-1b' to each side of the equation. b + -1b + c = 10 + -1b Combine like terms: b + -1b = 0 0 + c = 10 + -1b c = 10 + -1b Add '-1c' to each side of the equation. c + -1c = 10 + -1b + -1c Combine like terms: c + -1c = 0 0 = 10 + -1b + -1c Simplifying 0 = 10 + -1b + -1c The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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