Question

Solve the quadratic equation by completing the square
x² - 8x + 13 = 0
​

Answer 1

x = 4 + √3 or x = 4 - √3

Explanation:

Use quadratic formula with a=1, b=-8, c=13.

x=−b ± √b2 − 4ac / 2a

x= −(−8) ± √(−8)2 − 4(1)(13) / 2(1)

x= 8 ± √12 / 2

x= 4 + √3 or x= 4 − √3

Answer 2

x = 4 ±
`√(3)`

Explanation:

Given

x² - 8x + 13 = 0 ( subtract 13 from both sides )

x² - 8x = - 13

To complete the square

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

x² + 2(- 4)x + 16 = - 13 + 16

(x - 4)² = 3 ( take the square root of both sides )

x - 4 = ±
`√(3)` ( add 4 to both sides )

x = 4 ±
`√(3)`