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Simplifying (4a + -5c)(4a + -5c) = 0 Multiply (4a + -5c) * (4a + -5c) (4a * (4a + -5c) + -5c * (4a + -5c)) = 0 ((4a * 4a + -5c * 4a) + -5c * (4a + -5c)) = 0 Reorder the terms: ((-20ac + 16a2) + -5c * (4a + -5c)) = 0 ((-20ac + 16a2) + -5c * (4a + -5c)) = 0 (-20ac + 16a2 + (4a * -5c + -5c * -5c)) = 0 (-20ac + 16a2 + (-20ac + 25c2)) = 0 Reorder the terms: (-20ac + -20ac + 16a2 + 25c2) = 0 Combine like terms: -20ac + -20ac = -40ac (-40ac + 16a2 + 25c2) = 0 Solving -40ac + 16a2 + 25c2 = 0 Solving for variable 'a'. Factor a trinomial. (4a + -5c)(4a + -5c) = 0Subproblem 1
Set the factor '(4a + -5c)' equal to zero and attempt to solve: Simplifying 4a + -5c = 0 Solving 4a + -5c = 0 Move all terms containing a to the left, all other terms to the right. Add '5c' to each side of the equation. 4a + -5c + 5c = 0 + 5c Combine like terms: -5c + 5c = 0 4a + 0 = 0 + 5c 4a = 0 + 5c Remove the zero: 4a = 5c Divide each side by '4'. a = 1.25c Simplifying a = 1.25cSubproblem 2
Set the factor '(4a + -5c)' equal to zero and attempt to solve: Simplifying 4a + -5c = 0 Solving 4a + -5c = 0 Move all terms containing a to the left, all other terms to the right. Add '5c' to each side of the equation. 4a + -5c + 5c = 0 + 5c Combine like terms: -5c + 5c = 0 4a + 0 = 0 + 5c 4a = 0 + 5c Remove the zero: 4a = 5c Divide each side by '4'. a = 1.25c Simplifying a = 1.25cSolution
a = {1.25c, 1.25c}
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