Question 143032


{{{x^2+8 x=-15}}} Start with the given equation



Take half of the x coefficient {{{8}}} to get {{{4}}} (ie {{{(1/2)(8)=4}}}).


Now square {{{4}}} to get {{{16}}} (ie {{{(4)^2=(4)(4)=16}}})



{{{x^2+8 x+16=-15+16}}} Add this value to both sides



{{{x^2+8 x+16=1}}} Combine like terms



{{{(x+4)^2=1}}} Now factor {{{x^2+8x+16}}} to get {{{(x+4)^2}}}



{{{x+4=0+-sqrt(1)}}} Take the square root of both sides



{{{x+4=1}}} or {{{x+4=-1}}} Simplify



{{{x=-3}}} or {{{x=-5}}} Simplify  Subtract {{{4}}} from both sides in each case




So the solutions are {{{x=-3}}} or {{{x=-5}}} 




Notice if we graph we can see that the roots are {{{x=-3}}} and {{{x=-5}}}. So this verifies our answer.


{{{graph(500,500,-10,10,-10,10, x^2+8x+15)}}}