Question 180302
{{{x^2 + 6x = -7}}}
{{{x^2 + 6x + (6/2)^2 = -7 + (6/2)^2}}}
{{{(x + 3)^2 = -7 + 9}}}
{{{(x + 3)^2 = 2}}}
Take the square root of both sides
{{{x + 3 = sqrt(2)}}}
{{{x = sqrt(2) - 3}}}
{{{x = 1.414 - 3}}}
{{{x = -1.586}}}
and
{{{x + 3 = -(sqrt(2))}}}
{{{x = -(sqrt(2)) - 3}}}
{{{x = -4.414}}}
graphing:
 {{{ graph( 500, 500, -10, 10, -10, 10, x^2 + 6x + 7) }}}
One root lies between -1 and -2
The other root lies between -4 and -5