Question 106099
To complete the square you want to come to an equation that looks like:
{{{(x+a)^2}}}
If you expand that form and look for common terms in your equation,
{{{(x+a)^2=x^2+2ax+a^2}}}
Comparing with your equation,
{{{x^2+2ax+a^2=x^2+4x-21+Z}}}
Where Z is the constant I will add to both sides of my original equation to complete the square. 
Comparing the x term,
{{{2ax=4x}}}
{{{2a=4}}}
{{{a=2}}}
Comparing my constant terms,
{{{a^2=-21+Z}}}
{{{4=-21+Z}}}
{{{Z=25}}}
Going back to the original equation:
{{{x^2 + 4x - 21 = 0}}}
Add Z to both sides,
{{{x^2+4x-21+25= 25}}}
{{{x^2+4x+4= 25}}}
{{{(x+2)^2= 25}}}
Two solutions. 
{{{x+2=5)}}} and {{{x+2= -5}}} 
{{{x+2=5)}}}
{{{highlight(x=3)}}}
{{{x+2= -5}}}
{{{highlight(x=-7)}}}
Always check your answers.
{{{x^2 + 4x - 21 = 0}}}
{{{3^2 + 4(3) - 21 = 0}}}
{{{9+12-21=0}}}
{{{0=0}}}
Good answer.
{{{x^2 + 4x - 21 = 0}}}
{{{(-7)^2 + 4(-7) - 21 = 0}}}
{{{49-28-21=0}}}
{{{0=0}}}
Good answer. 
x=3 and x=-7.