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:
- Half of the coefficient of x = -8/2 = -4
- Taking the square = (-4)² = 16
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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