Given:
color(white)("XXX")-2x^2-4x+30=0XXX−2x2−4x+30=0
Before completing the square, simplify by dividing everything (on both sides) by (-2)(−2)
color(white)("XXX")x^2+2x-15=0XXXx2+2x−15=0
Move the constant to the right side (by adding 1515 to both sides)
color(white)("XXX")color(blue)(x^2+2x)=15XXXx2+2x=15
Now to complete the square
[
(color(white)("XXXXXX")"Since "(x+a)^2 = color(blue)(x^2+2ax)+a^2),
(color(white)("XXXXXX")"If "color(blue)(x^2+2x)" are the first two terms of a squared binomial"),
(color(white)("XXXXXX")"Then "a=1" in the general expansion"),
(color(white)("XXXXXX")"and we will need to add "color(red)(1)" to both sides"),
(color(white)("XXXXXX")"to get a squared binomial on the left side:"),
(color(white)("XXX")color(blue)(x^2+2x)color(red)(+1) = 15color(red)(+1)),
(" "),
(color(white)("XXX")"Re-writing as a squared binomial (and a simplified constant on the right side):"),
(color(white)("XXX")(x+1)^2=16)
:}
Take the square root of both sides:
color(white)("XXX")x+1=+-4 (don't forget both roots of 16)
Subtract 1 from both sides:
color(white)("XXX")x=3 or x=-5
