Question

What number should be added to both sides of the equation to complete the square?

x2 – 6x = 5

What number should be added to both sides of the equation to complete the square?

x2 – 6x = 5

Answer 1

\(\sf\underline{Completing~squares}\)

\(\large ax^2+bx=0\)

Divide the whole equation by the coefficient of \(x^2\).
\(\large x^2+\Large\frac{b}{a}\large x=0\)

Divide the coefficient of \(x\) by 2.
\(\large x^2+\Large\frac{b}{2a}\large x=0\)

Add the squared new coefficient of \(x\) to both sides.
\(\large x^2+\Large\frac{b}{2a}\large x+(\Large\frac{b}{2a})\large^2=0+\Large(\frac{b}{2a})\large^2\)
\(\large(x+\Large\frac{b}{2a})\large^2=0+\Large(\frac{b}{2a})\large^2\)