#### Show that x^2 + 6x + 11 can be written as (x + p)^2 + q where p and q are integers to be found.

Anonymous

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Anonymous

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Krishna

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Step 1: Note-down the given quadratic equation and compare it with the standard form ax^2 + bx + c

EXAMPLE: 2x^2 - 3x - (k+1)

ax^2 + bx + c

Where a = 2, b = - 3 and c = - (k+1)

Step 2: Calculate the B and C values

NOTE: ax^2 + bx + c write in the form of the (Ax+B)^2+C\ \ \ \ .

Comparing this two equations shows that

*b* = 2*B* or B = \frac{b}{2} and c = B^2 + C or C = c - B^2 since A = 1

EXAMPLE: x^2 - 6x + 13

B = \frac{-6}{2} and C = 13 - (-3)^2

B = -3 and C = 4

Step 3: Substitute these values in the equation (*x* + *B*)2 + *C*.

EXAMPLE: (x - 3)^2 + 4

Step 4: Compare the two equations and note down the unknown values

EXAMPLE: (x - 3)^2 + 4 = (x+p)^2+q