Question 243623


{{{9x^2+6x+1=64}}} Start with the given equation.



{{{9x^2+6x+1-64=0}}} Subtract 64 from both sides.



{{{9x^2+6x-63=0}}} Combine like terms.



Notice that the quadratic {{{9x^2+6x-63}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=9}}}, {{{B=6}}}, and {{{C=-63}}}



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(9)(-63) ))/(2(9))}}} Plug in  {{{A=9}}}, {{{B=6}}}, and {{{C=-63}}}



{{{x = (-6 +- sqrt( 36-4(9)(-63) ))/(2(9))}}} Square {{{6}}} to get {{{36}}}. 



{{{x = (-6 +- sqrt( 36--2268 ))/(2(9))}}} Multiply {{{4(9)(-63)}}} to get {{{-2268}}}



{{{x = (-6 +- sqrt( 36+2268 ))/(2(9))}}} Rewrite {{{sqrt(36--2268)}}} as {{{sqrt(36+2268)}}}



{{{x = (-6 +- sqrt( 2304 ))/(2(9))}}} Add {{{36}}} to {{{2268}}} to get {{{2304}}}



{{{x = (-6 +- sqrt( 2304 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{x = (-6 +- 48)/(18)}}} Take the square root of {{{2304}}} to get {{{48}}}. 



{{{x = (-6 + 48)/(18)}}} or {{{x = (-6 - 48)/(18)}}} Break up the expression. 



{{{x = (42)/(18)}}} or {{{x =  (-54)/(18)}}} Combine like terms. 



{{{x = 7/3}}} or {{{x = -3}}} Simplify. 



So the solutions are {{{x = 7/3}}} or {{{x = -3}}}