Question 264648


{{{7x^2-x-6=0}}} Start with the given equation.



Notice that the quadratic {{{7x^2-x-6}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=7}}}, {{{B=-1}}}, 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 = (-(-1) +- sqrt( (-1)^2-4(7)(-6) ))/(2(7))}}} Plug in  {{{A=7}}}, {{{B=-1}}}, and {{{C=-6}}}



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



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



{{{x = (1 +- sqrt( 1--168 ))/(2(7))}}} Multiply {{{4(7)(-6)}}} to get {{{-168}}}



{{{x = (1 +- sqrt( 1+168 ))/(2(7))}}} Rewrite {{{sqrt(1--168)}}} as {{{sqrt(1+168)}}}



{{{x = (1 +- sqrt( 169 ))/(2(7))}}} Add {{{1}}} to {{{168}}} to get {{{169}}}



{{{x = (1 +- sqrt( 169 ))/(14)}}} Multiply {{{2}}} and {{{7}}} to get {{{14}}}. 



{{{x = (1 +- 13)/(14)}}} Take the square root of {{{169}}} to get {{{13}}}. 



{{{x = (1 + 13)/(14)}}} or {{{x = (1 - 13)/(14)}}} Break up the expression. 



{{{x = (14)/(14)}}} or {{{x =  (-12)/(14)}}} Combine like terms. 



{{{x = 1}}} or {{{x = -6/7}}} Simplify. 



So the solutions are {{{x = 1}}} or {{{x = -6/7}}}