Question

Solve the following quadratic by
completing the square.
y = x2 – 8x + 5

Answer 1

x = 4 ±
`√(11)`

Explanation:

To solve the equation let y = 0 , that is

x² - 8x + 5 = 0 ( subtract 5 from both sides )

x² - 8x = - 5

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = - 5 + 16

(x - 4)² = 11 ( take the square root of both sides )

x - 4 = ±
`√(11)` ( add 4 to both sides )

x = 4 ±
`√(11)`

Answer 2

x = 4 ± √11

Explanation:

hello :

x²-8x+5= x² -2(4 )(x)+5

x²-8x+5= x² -2(4 )(x)+5 = ( x² -2(4 )(x) +4²) -4²+5

= (x-4)²-11 .....( completing the square )

x²-8x+5= 0 means : (x-4)²-11 = 0

(x-4)²=11 but : 11 = (√11)² = ( - √11)²

x-4 =√11 or x-4 = -√11

x = 4 ± √11