Question 148103
{{{2x+(x+1)^2=8}}} Start with the given equation.



{{{2x+x^2+2x+1=8}}} Foil.



{{{2x+x^2+2x+1-8=0}}} Subtract 8 from both sides.



{{{x^2+4x-7=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=4}}}, and {{{c=-7}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(4) +- sqrt( (4)^2-4(1)(-7) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=4}}}, and {{{c=-7}}}



{{{x = (-4 +- sqrt( 16-4(1)(-7) ))/(2(1))}}} Square {{{4}}} to get {{{16}}}. 



{{{x = (-4 +- sqrt( 16--28 ))/(2(1))}}} Multiply {{{4(1)(-7)}}} to get {{{-28}}}



{{{x = (-4 +- sqrt( 16+28 ))/(2(1))}}} Rewrite {{{sqrt(16--28)}}} as {{{sqrt(16+28)}}}



{{{x = (-4 +- sqrt( 44 ))/(2(1))}}} Add {{{16}}} to {{{28}}} to get {{{44}}}



{{{x = (-4 +- sqrt( 44 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-4 +- 2*sqrt(11))/(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>)  



{{{x = (-4)/(2) +- (2*sqrt(11))/(2)}}} Break up the fraction.  



{{{x = -2 +- sqrt(11)}}} Reduce.  



{{{x = -2+sqrt(11)}}} or {{{x = -2-sqrt(11)}}} Break up the expression.  



So our answers are {{{x = -2+1*sqrt(11)}}} or {{{x = -2-1*sqrt(11)}}} 



which approximate to {{{x=1.317}}} or {{{x=-5.317}}}