The value of a = 6, b = 1/2 and c = -5/2
In this question, we have been given an equation,
6x² + 6x − 1 = a(x + b)² + c.
We need to find the value of a, b and c.
6x² + 6x − 1 = a(x + b)² + c
6x² + 6x − 1 = a(x^2 + 2bx + b²) + c
6x² + 6x − 1 = ax^2 + 2abx + ab² + c
Comparing coefficient of x^2, x and constant term,
1) a = 6
2) 2ab = 6
Substitute above value of a ,
2(6)b = 6
b = 1/2
3) ab^2 + c = -1
substitute above value of a and b
6(1/2)^2 + c = -1
6 * 1/4 + c = -1
3/2 + c = -1
c = -1 - 3/2
c = -(1 + 3/2)
c = -5/2
Therefore, the value of a = 6, b = 1/2 and c = -5/2
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