Question 178397


{{{x^2+8x+7=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=8}}}, 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 = (-(8) +- sqrt( (8)^2-4(1)(7) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=8}}}, and {{{c=7}}}



{{{x = (-8 +- sqrt( 64-4(1)(7) ))/(2(1))}}} Square {{{8}}} to get {{{64}}}. 



{{{x = (-8 +- sqrt( 64-28 ))/(2(1))}}} Multiply {{{4(1)(7)}}} to get {{{28}}}



{{{x = (-8 +- sqrt( 36 ))/(2(1))}}} Subtract {{{28}}} from {{{64}}} to get {{{36}}}



{{{x = (-8 +- sqrt( 36 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-8 +- 6)/(2)}}} Take the square root of {{{36}}} to get {{{6}}}. 



{{{x = (-8 + 6)/(2)}}} or {{{x = (-8 - 6)/(2)}}} Break up the expression. 



{{{x = (-2)/(2)}}} or {{{x =  (-14)/(2)}}} Combine like terms. 



{{{x = -1}}} or {{{x = -7}}} Simplify. 



So the answers are {{{x = -1}}} or {{{x = -7}}}