Question 271993
{{{y^2 +4y +4 =7}}}
Solving quadratic equations start with getting one side of the equation equal to zero. So we'll subtract 7 from each side:
{{{y^2 + 4y -3 = 0}}}
Next we would either factor the non-zero side or use the Quadratic Formula. Normally I prefer factoring but this equation does not factor. So we must use the Quadratic Formula, {{{x = (-b +- sqrt(b^2 - 4ac))/(2a)}}}. Using this on our equation we get:
{{{y = (-(4) +- sqrt((4)^2 - 4(1)(-3)))/(2(1))}}}
Simplifying we get:
{{{y = (-4 +- sqrt(16 - 4(1)(-3)))/2}}}
{{{y = (-4 +- sqrt(16 + 12))/2}}}
{{{y = (-4 +- sqrt(28))/2}}}
{{{y = (-4 +- sqrt(4*7))/2}}}
{{{y = (-4 +- sqrt(4)*sqrt(7))/2}}}
{{{y = (-4 +- 2*sqrt(7))/2}}}
{{{y = (2(-2 +- sqrt(7)))/2}}}
{{{y = (cross(2)(-2 +- sqrt(7)))/cross(2)}}}
{{{y = -2 +- sqrt(7)}}}