Express x²-8x+5 in the form (x-a)²-b where a and b are integers

The expression of x²-8x+5 in the form (x-a)²-b where a and b are integers is (x-4)² - 11

Given the quadratic equation x²-8x+5

First, we need to complete the square x²-8x

To do that, we will add and subtract the square of the half of coefficient of x in the expression:

Hence the equation becomes:

= x²-8x + 16 - 16 + 5

= x²-4x -4x+ 16 - 11

= x(x-4)-4(x-4 ) - 11

= (x-4)(x-4) - 11

= (x-4)² - 11

Hence the expression of x²-8x+5 in the form (x-a)²-b where a and b are integers is (x-4)² - 11

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x^2-8x+16-11= (x-4)^2-11