Completing The Squares

Question

7a² +14a + 86 = 9

Answer 1

Writing this in standard form,

 

7x² + 14x + 86 = 9

 

7x² + 14x + 77 = 0

 

Simplify this by diving by 7.

 

x² + 2x + 11 = 0

 

In this standard form, A=1, B=2, C=11

 

To complete the square, add B²/(4A²) to both sides, and move C to the right side.

 

B²/(4A²) = 2²/(4*1²) = 1

 

x² + 2x + 1 = -11 + 1 = -10

 

Note that x² + 2x + 1 is a perfect square, since x² + 2x + 1 = (x+1)²

 

Finally, the complete square is:

 

(x+1)² = -10

 

Note x must be a complex number.