Completing a square

Completing the square means that you take the coefficient in front of the "x", dividing by 2, squaring that, and then adding it to both sides of the equation:

**ax ^{2} + bx = c**

**ax ^{2} + bx + (b/2)^{2} = c + (b/2)^{2}**

in your example that number is 15...

so

x^{2} + 15x + (15/2)^{2} = (15/2)^{2} - 26

(15/2)^{2} = 225/4 and 26 = 104/4 their difference is then 121/4

and you get

**[x + (15/2)] ^{2} - 121/4 = 0**

to check multiply it back out

[x + (15/2)][x + (15/2)] = 121/4

x^{2} + (15/2)x + (15/2)x + 225/4 = 121/4

x^{2} + 15x = 121/4 - 225/4 = -104/4

x^{2} + 15x = -26