Question 174873

{{{y^2+4y+4=7}}} Start with the given equation.



{{{y^2+4y+4-7=0}}} Subtract 7 from both sides.



{{{y^2+4y-3=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ay^2+by+c}}} where {{{a=1}}}, {{{b=4}}}, and {{{c=-3}}}



Let's use the quadratic formula to solve for y



{{{y = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{y = (-(4) +- sqrt( (4)^2-4(1)(-3) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=4}}}, and {{{c=-3}}}



{{{y = (-4 +- sqrt( 16-4(1)(-3) ))/(2(1))}}} Square {{{4}}} to get {{{16}}}. 



{{{y = (-4 +- sqrt( 16--12 ))/(2(1))}}} Multiply {{{4(1)(-3)}}} to get {{{-12}}}



{{{y = (-4 +- sqrt( 16+12 ))/(2(1))}}} Rewrite {{{sqrt(16--12)}}} as {{{sqrt(16+12)}}}



{{{y = (-4 +- sqrt( 28 ))/(2(1))}}} Add {{{16}}} to {{{12}}} to get {{{28}}}



{{{y = (-4 +- sqrt( 28 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{y = (-4 +- 2*sqrt(7))/(2)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{y = (-4)/(2) +- (2*sqrt(7))/(2)}}} Break up the fraction.  



{{{y = -2 +- sqrt(7)}}} Reduce.  



{{{y = -2+sqrt(7)}}} or {{{y = -2-sqrt(7)}}} Break up the expression.  



So the answers are {{{y = -2+sqrt(7)}}} or {{{y = -2-sqrt(7)}}} 



which approximate to {{{y=0.646}}} or {{{y=-4.646}}}