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Simplifying (4a + -7)(-7a + 4) = 0 Reorder the terms: (-7 + 4a)(-7a + 4) = 0 Reorder the terms: (-7 + 4a)(4 + -7a) = 0 Multiply (-7 + 4a) * (4 + -7a) (-7(4 + -7a) + 4a * (4 + -7a)) = 0 ((4 * -7 + -7a * -7) + 4a * (4 + -7a)) = 0 ((-28 + 49a) + 4a * (4 + -7a)) = 0 (-28 + 49a + (4 * 4a + -7a * 4a)) = 0 (-28 + 49a + (16a + -28a2)) = 0 Combine like terms: 49a + 16a = 65a (-28 + 65a + -28a2) = 0 Solving -28 + 65a + -28a2 = 0 Solving for variable 'a'. Factor a trinomial. (-7 + 4a)(4 + -7a) = 0Subproblem 1
Set the factor '(-7 + 4a)' equal to zero and attempt to solve: Simplifying -7 + 4a = 0 Solving -7 + 4a = 0 Move all terms containing a to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + 4a = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 4a = 0 + 7 4a = 0 + 7 Combine like terms: 0 + 7 = 7 4a = 7 Divide each side by '4'. a = 1.75 Simplifying a = 1.75Subproblem 2
Set the factor '(4 + -7a)' equal to zero and attempt to solve: Simplifying 4 + -7a = 0 Solving 4 + -7a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -7a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7a = 0 + -4 -7a = 0 + -4 Combine like terms: 0 + -4 = -4 -7a = -4 Divide each side by '-7'. a = 0.5714285714 Simplifying a = 0.5714285714Solution
a = {1.75, 0.5714285714}
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