Question 315566


{{{4x^2+9x=9}}} Start with the given equation.



{{{4x^2+9x-9=0}}} Subtract 9 from both sides.



Notice that the quadratic {{{4x^2+9x-9}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=4}}}, {{{B=9}}}, and {{{C=-9}}}



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(4)(-9) ))/(2(4))}}} Plug in  {{{A=4}}}, {{{B=9}}}, and {{{C=-9}}}



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



{{{x = (-9 +- sqrt( 81--144 ))/(2(4))}}} Multiply {{{4(4)(-9)}}} to get {{{-144}}}



{{{x = (-9 +- sqrt( 81+144 ))/(2(4))}}} Rewrite {{{sqrt(81--144)}}} as {{{sqrt(81+144)}}}



{{{x = (-9 +- sqrt( 225 ))/(2(4))}}} Add {{{81}}} to {{{144}}} to get {{{225}}}



{{{x = (-9 +- sqrt( 225 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{x = (-9 +- 15)/(8)}}} Take the square root of {{{225}}} to get {{{15}}}. 



{{{x = (-9 + 15)/(8)}}} or {{{x = (-9 - 15)/(8)}}} Break up the expression. 



{{{x = (6)/(8)}}} or {{{x =  (-24)/(8)}}} Combine like terms. 



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



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