Find the values of a and b such that x^2-4x+9=(x+a)^2+b

  a = -2; b = 5

Step-by-step explanation:

Expanding the right side of the given equation, we have ...

  x^2 -4x +9 = x^2 +2ax +a^2 +b

Comparing coefficients, we see ...

  -4 = 2a . . . . . coefficient of x term

  9 = a^2 +b . . . constant term

The first of these tells us ...

  -2 = a . . . . divide by 2

The second of these tells us ...

  9 = (-2)^2 +b . . . substitute for a

  5 = b . . . . subtract 4

The values of a and b are (a, b) = (-2, 5).

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step-by-step explanation: