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

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

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Answer 1 · 2017-03-17T14:07:48

$x = - 0.76393202 or x = - 5.23606797$ $x=-0.76393202 or x=-5.23606797$

Explanation:

$C o m m e n c i n g$ $color(red)(Commenci ng)$ $c o m p l e t i n g$ $color(red)(compl e ti ng)$ $t h e$ $color(red)(the)$ $s q u a r e$ $color(red)(squ are)$ $m e t h o d$ $color(red)(method)$ $n o w,$ $color(red)(now,)$

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

${(a x \pm b)}^{2} = a x^{2} \pm 2 a b x + b^{2}$ $(ax+-b)^2 = ax^2+-2abx+b^2$

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

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

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

$x^{2} + 6 x = - 4$ $x^2+6x=-4$

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

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

5) Square root both sides,

$x + 3 = \pm \sqrt{5}$ $x+3=+-sqrt(5)$

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

$x = \pm \sqrt{5} - 3$ $x=+-sqrt5-3$

7) Calculate the two values of $x$ $x$ ,

$x = - 0.76393202 or x = - 5.23606797$ $x=-0.76393202 or x=-5.23606797$

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

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How do you solve using the completing the square method x2+6x+4=0x^2+6x+4=0?

1 Answer

Explanation:

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