Question 180789


{{{x^2-6x-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=-6}}}, 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 = (-(-6) +- sqrt( (-6)^2-4(1)(-7) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-6}}}, and {{{c=-7}}}



{{{x = (6 +- sqrt( (-6)^2-4(1)(-7) ))/(2(1))}}} Negate {{{-6}}} to get {{{6}}}. 



{{{x = (6 +- sqrt( 36-4(1)(-7) ))/(2(1))}}} Square {{{-6}}} to get {{{36}}}. 



{{{x = (6 +- sqrt( 36--28 ))/(2(1))}}} Multiply {{{4(1)(-7)}}} to get {{{-28}}}



{{{x = (6 +- sqrt( 36+28 ))/(2(1))}}} Rewrite {{{sqrt(36--28)}}} as {{{sqrt(36+28)}}}



{{{x = (6 +- sqrt( 64 ))/(2(1))}}} Add {{{36}}} to {{{28}}} to get {{{64}}}



{{{x = (6 +- sqrt( 64 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (6 +- 8)/(2)}}} Take the square root of {{{64}}} to get {{{8}}}. 



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



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



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



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