X^2+15x=-26

Question

Completing a square

Answer 1

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:

ax² + bx = c

ax² + bx + (b/2)² = c + (b/2)²

in your example that number is 15...

so

x² + 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

x² + (15/2)x + (15/2)x + 225/4 = 121/4

x² + 15x = 121/4 - 225/4 = -104/4

x² + 15x = -26