Question 4350
Begin by adding 5 to each side to set up the "completing the square" process.


{{{x^2 + 4x - 5 = 0}}}

{{{x^2 + 4x  =  5}}}

{{{x^2 + 4x + _____ = 5 + _____}}}


Take half of the 4 and square, which is 2 squared, or 4.  Add 4 to each side of the equation to create a perfect square trinomial on the left side.


{{{x^2 + 4x + 4 = 5 + 4}}}

{{{ (x+2)^2 = 9 }}}


Take the square root of both sides:


{{{x + 2 = 0 +- 3}}}


Subtract 2 from each side:

{{{x +2 - 2 = -2 +- 3}}}
{{{x = -2 +- 3}}}


In the first case, x = -2 + 3 = 1
In the second case, x = -2 - 3 = -5


Check answers:  {{{x^2 + 4x - 5 = 0}}}

For x = 1, {{{1^2 + 4*1 - 5 = 0}}}
For x = -5, {{{(-5)^2 + 4*(-5) - 5 = 0}}}


Both answers check!


R^2 at SCC