Solve x2-4x-7=0 by completing the square

x = 2 ±

Step-by-step explanation:

Given

x² - 4x - 7 = 0 ( add 7 to both sides )

x² - 4x = 7

To complete the square

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

x² + 2(- 2)x + (- 2)² = 7 + (- 2)²

(x - 2)² = 7 + 4 = 11 ( take the square root of both sides )

x - 2 = ± ( add 2 to both sides )

x = 2 ± ← exact solutions

Let the original 2-digit number be xy.
Because 5 times the sum of the digits is 13 less than the number, therefore
5(x + y) = 10x + y - 13 
5x + 5y = 10x + y - 13
-5x + 4y = - 13             (1)

The number with reversed digits is yx.
Because 4 times the sum of the digits is 21 less than the reversed 2-digit number, therefore
4(x + y) = 10y + x - 21
4x + 4y = 10y + x - 21
3x - 6y = -21
x - 2y = -7
x = 2y - 7                 (2)

Substitute (2) into (1).
-5(2y - 7) + 4y = -13
-10y + 35 + 4y = -13
-6y = -48
y = 8

From (3), obtain
x = 2*8 - 7 = 9

Answers:
The original 2-digit number is 98
The reversed 2-digit number is 89
The difference between the original and the reversed 2-digit numbers is
98 - 89 = 9