How do I solve x^2 + 5x + 4 using "Completing the Square Method"?

Question

Please show working out
I understand that it can just be solved in your head (x+4)(x+1) but I can't get that answer by using that method

Answer 1

Its easy jst try to keep it in the form of (a+b)^2=a^2+2ab+b^2

=(x^2)+2*x*(5/2)+(25/4)-(25/4)+4 (keeping +-(25/4))

=(x^2+2*x*(5/2)+(5/2)^2)-(25/4)+4 (arranging it in the form of a^2+2ab+b^2 )

=(x+5/2)^2-9/4



Hope it helps

:)

Answer 2

if you are solving, there must be an equal sign. All you've given is an expression. Can I assume you to mean that the expression is equal to zero? If so . . .



x^2 + 5x + 4 = 0



x^2 + 5x = -4



x^2 + 5x + 25/4 = -4 + 25/4



(x + 5/2)^2 = -16/4 + 25/4 = 9/4



x + 5/2 = ±√(9/4)



x + 5/2 = ± 3/2



x = -5/2 + 3/2 or x = -5/2 - 3/2



x = -1 or x = -4



that's it! ;)