How do you solve using the completing the square method $x^2+6x+4=0$ ?

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Answer 1 · 2017-03-17T14:07:48

$x=-0.76393202 or x=-5.23606797$

$color(red)(Commenci ng)$ $color(red)(compl e ti ng)$ $color(red)(the)$ $color(red)(squ are)$ $color(red)(method)$ $color(red)(now,)$

1) Know the formula for the perfect quadratic square, which is,

$(ax+-b)^2 = ax^2+-2abx+b^2$

2) Figure out your $a and b$ values,

$a=$ coefficient of $x^2$ , which is $1$ .
$color(red)(b=6/(2(1)) = 3)$

3) Move the $4$ over to the right hand side,

$x^2+6x=-4$

4) Add $color(red)(b^2)$ on both sides of the equation, giving you an overall net of 0, hence not affecting the result of the equation,

$x^2+6x+color(red)(3^2)=-4+color(red)(3^2)$
$(x+3)^2=5$

5) Square root both sides,

$x+3=+-sqrt(5)$

6) Move the $3$ over to the right side,

$x=+-sqrt5-3$

7) Calculate the two values of $x$ ,

$x=-0.76393202 or x=-5.23606797$

How do you solve using the completing the square method x^2+6x+4=0x^2+6x+4=0?