Question 569954


{{{x^2-9x-22=0}}} Start with the given equation.



Notice that the quadratic {{{x^2-9x-22}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-9}}}, and {{{C=-22}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(-9) +- sqrt( (-9)^2-4(1)(-22) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-9}}}, and {{{C=-22}}}



{{{x = (9 +- sqrt( (-9)^2-4(1)(-22) ))/(2(1))}}} Negate {{{-9}}} to get {{{9}}}. 



{{{x = (9 +- sqrt( 81-4(1)(-22) ))/(2(1))}}} Square {{{-9}}} to get {{{81}}}. 



{{{x = (9 +- sqrt( 81--88 ))/(2(1))}}} Multiply {{{4(1)(-22)}}} to get {{{-88}}}



{{{x = (9 +- sqrt( 81+88 ))/(2(1))}}} Rewrite {{{sqrt(81--88)}}} as {{{sqrt(81+88)}}}



{{{x = (9 +- sqrt( 169 ))/(2(1))}}} Add {{{81}}} to {{{88}}} to get {{{169}}}



{{{x = (9 +- sqrt( 169 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (9 +- 13)/(2)}}} Take the square root of {{{169}}} to get {{{13}}}. 



{{{x = (9 + 13)/(2)}}} or {{{x = (9 - 13)/(2)}}} Break up the expression. 



{{{x = (22)/(2)}}} or {{{x =  (-4)/(2)}}} Combine like terms. 



{{{x = 11}}} or {{{x = -2}}} Simplify. 



So the solutions are {{{x = 11}}} or {{{x = -2}}}