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Simplifying
(7a + 5t)(7a + -5t) = 0
Multiply (7a + 5t) * (7a + -5t)
(7a * (7a + -5t) + 5t * (7a + -5t)) = 0
((7a * 7a + -5t * 7a) + 5t * (7a + -5t)) = 0
Reorder the terms:
((-35at + 49a2) + 5t * (7a + -5t)) = 0
((-35at + 49a2) + 5t * (7a + -5t)) = 0
(-35at + 49a2 + (7a * 5t + -5t * 5t)) = 0
(-35at + 49a2 + (35at + -25t2)) = 0
Reorder the terms:
(-35at + 35at + 49a2 + -25t2) = 0
Combine like terms: -35at + 35at = 0
(0 + 49a2 + -25t2) = 0
(49a2 + -25t2) = 0
Solving
49a2 + -25t2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '25t2' to each side of the equation.
49a2 + -25t2 + 25t2 = 0 + 25t2
Combine like terms: -25t2 + 25t2 = 0
49a2 + 0 = 0 + 25t2
49a2 = 0 + 25t2
Remove the zero:
49a2 = 25t2
Divide each side by '49'.
a2 = 0.5102040816t2
Simplifying
a2 = 0.5102040816t2
Take the square root of each side:
a = {-0.714285714t, 0.714285714t}
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