Question 319174


{{{8x^2+22x-6=0}}} Start with the given equation.



Notice that the quadratic {{{8x^2+22x-6}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=8}}}, {{{B=22}}}, and {{{C=-6}}}



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



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



{{{x = (-(22) +- sqrt( (22)^2-4(8)(-6) ))/(2(8))}}} Plug in  {{{A=8}}}, {{{B=22}}}, and {{{C=-6}}}



{{{x = (-22 +- sqrt( 484-4(8)(-6) ))/(2(8))}}} Square {{{22}}} to get {{{484}}}. 



{{{x = (-22 +- sqrt( 484--192 ))/(2(8))}}} Multiply {{{4(8)(-6)}}} to get {{{-192}}}



{{{x = (-22 +- sqrt( 484+192 ))/(2(8))}}} Rewrite {{{sqrt(484--192)}}} as {{{sqrt(484+192)}}}



{{{x = (-22 +- sqrt( 676 ))/(2(8))}}} Add {{{484}}} to {{{192}}} to get {{{676}}}



{{{x = (-22 +- sqrt( 676 ))/(16)}}} Multiply {{{2}}} and {{{8}}} to get {{{16}}}. 



{{{x = (-22 +- 26)/(16)}}} Take the square root of {{{676}}} to get {{{26}}}. 



{{{x = (-22 + 26)/(16)}}} or {{{x = (-22 - 26)/(16)}}} Break up the expression. 



{{{x = (4)/(16)}}} or {{{x =  (-48)/(16)}}} Combine like terms. 



{{{x = 1/4}}} or {{{x = -3}}} Simplify. 



So the solutions are {{{x = 1/4}}} or {{{x = -3}}}