Answer:
a = 6 or 9
Step-by-step explanation:
The "a", "b", and "c" of the quadratic formula are the coefficients of a², a, and the constant term in the given equation:
... a = 2, b = -30, c = 108
Then the quadratic formula tells you the solutions are ...
... (-b ± √(b² -4ac))/(2a)
... = (-(-30) ± √((-30)² -4(2)(108)))/(2(2))
... = (30 ± √(900 -864))/4
... = (30 ± √36)/4
... = (30 ± 6)/4 = {24, 36}/4
... = {6, 9}
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The a variable should not be confused with the "a" that is used to name the coefficient of the square of the variable in the quadratic formula. If it is too confusing, rewrite one or the other. For example, you could write ...
... The solution to pa² +qa +r = 0 is ... a = (-q ± √(q²-4pr))/(2p)
where p=2, q=-30, r=108 in the given equation.
