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X^2+15x=-26

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1 Answer

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