Solve by completing the square: x^2 + 10x + 13 = 0?

x^2 + 10x + 13 = 0
x^2 + 5x + 5x + 13 = 0
(x + 5)^2 - 12 = 0
(x + 5)^2 = 12
x + 5 = ±√12
x + 5 ≈ ±3.46

x + 5 ≈ 3.46
x ≈ 3.46 - 5
x ≈ -1.54

x + 5 ≈ -3.46
x ≈ -3.46 - 5
x ≈ -8.46

∴ x ≈ -8.46 , -1.54

xÂ² + 10x = - 13
x² + 5x = - 13 + 5²
x² + 5x = - 13 + 25
(x + 5)² = 12
x + 5 = 3.46412

Values of x:
x = 3.46412 - 5, x = - 1.5359
x = - 3.46412 - 5, x = - 8.4641

Answer: x = - 1.5359, - 8.4641

Proof where x = - 1.5359:
(- 1.5359)² + 10(- 1.5359) = - 13
2.359 - 15.359 = - 13
- 13 = - 13

Proof where x = - 8.4641:
(- 8.4641)² + 10(- 8.4641) = - 13
71.641 - 84.641 = - 13
- 13 = - 13

x^2 + 10x = -13

now divide 10 by 2 and square that answer, you should get 10/2=5 5^2=25

x^2 + 10x +25 = -13 + 25
x^2 + 10x +25 = 12
(x+5)^2=12
squareroot(x+5)^2 = squareroot12
x+5= (+-)12
x=-5 +12
x=7********
or
x=-5-12
x=-17**********

sorry, i don't know how to make all the shortcut symbols

+or-vb^2-4ac........>formula
+or-v100-52=+or-v48=+or-4v3

x=-10+underroot of 48/2
x=-10-underroot of 48/2

x² + 10x + 25 = 25 - 13
(x + 5)² = 12
x + 5 = ± √12
x = - 5 ± 2√3