How do you solve $x(x+6)=-2$ using the quadratic formula?

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Answer 1 · 2017-10-29T11:58:42

$x= -0.354$
OR
$x = -5.645$

$x(x+6)=-2$

Writing it in standard form:

$x^2 +6x+2=0$

Compare with equation $ax^2 +bx+c=0$

$a = 1$
$b=6$
$c=2$

Quadratic formula:
$x=( -b +-sqrt(b^2 -4ac))/(2a)$

$x=-0.354248688~~-0.354$ ---truncated and approximate value.

Or

$x =-5.645751311~~-5.645$ ---truncated and approximate value.

$therefore x= -0.354$
OR
$x = -5.645$

Answer 2 · 2017-10-29T12:05:32

$x = -3 + root2 7 or approx -0.3542...$
$x = -3 - root2 7 or approx -5.6457...$

Expand and rearnage;
$x^2 + 6x = -2$
$x^2 + 6x + 2 = 0$

Then apply to the quadratic formula;
$a =1, b = 6, c=2$

$x = (-6+root2 ( 6^2 - ( 4*1*2) ))/2$
or $x = (-6-root2 ( 6^2 - ( 4*1*2) ))/2$

To give
$x = (-6+root2 ( 28 ))/2$
or $x = (-6-root2 ( 28 ))/2$

Hence
$x = (-6+2root2 ( 7 ))/2$
or $x = (-6-2root2 ( 7 ))/2$

Finally giving;
$x = -3 + root2 7 or approx -0.3542...$
$x = -3 - root2 7 or approx -5.6457...$

How do you solve x(x+6)=-2x(x+6)=-2 using the quadratic formula?