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Simplifying
(6a + 5d)(6a + -5d) = 0
Multiply (6a + 5d) * (6a + -5d)
(6a * (6a + -5d) + 5d * (6a + -5d)) = 0
((6a * 6a + -5d * 6a) + 5d * (6a + -5d)) = 0
Reorder the terms:
((-30ad + 36a2) + 5d * (6a + -5d)) = 0
((-30ad + 36a2) + 5d * (6a + -5d)) = 0
(-30ad + 36a2 + (6a * 5d + -5d * 5d)) = 0
(-30ad + 36a2 + (30ad + -25d2)) = 0
Reorder the terms:
(-30ad + 30ad + 36a2 + -25d2) = 0
Combine like terms: -30ad + 30ad = 0
(0 + 36a2 + -25d2) = 0
(36a2 + -25d2) = 0
Solving
36a2 + -25d2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '25d2' to each side of the equation.
36a2 + -25d2 + 25d2 = 0 + 25d2
Combine like terms: -25d2 + 25d2 = 0
36a2 + 0 = 0 + 25d2
36a2 = 0 + 25d2
Remove the zero:
36a2 = 25d2
Divide each side by '36'.
a2 = 0.6944444444d2
Simplifying
a2 = 0.6944444444d2
Take the square root of each side:
a = {-0.833333333d, 0.833333333d}
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