Question 277032
{{{4.9t^2 + 20t - 158.4=0}}} Start with the given equation



{{{49t^2 + 200t - 1584=0}}} Multiply every term by 10 to make every number a whole number (ie move the decimal one spot to the right).



Notice that the quadratic {{{49t^2+200t-1584}}} is in the form of {{{At^2+Bt+C}}} where {{{A=49}}}, {{{B=200}}}, and {{{C=-1584}}}



Let's use the quadratic formula to solve for "t":



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



{{{t = (-(200) +- sqrt( (200)^2-4(49)(-1584) ))/(2(49))}}} Plug in  {{{A=49}}}, {{{B=200}}}, and {{{C=-1584}}}



{{{t = (-200 +- sqrt( 40000-4(49)(-1584) ))/(2(49))}}} Square {{{200}}} to get {{{40000}}}. 



{{{t = (-200 +- sqrt( 40000--310464 ))/(2(49))}}} Multiply {{{4(49)(-1584)}}} to get {{{-310464}}}



{{{t = (-200 +- sqrt( 40000+310464 ))/(2(49))}}} Rewrite {{{sqrt(40000--310464)}}} as {{{sqrt(40000+310464)}}}



{{{t = (-200 +- sqrt( 350464 ))/(2(49))}}} Add {{{40000}}} to {{{310464}}} to get {{{350464}}}



{{{t = (-200 +- sqrt( 350464 ))/(98)}}} Multiply {{{2}}} and {{{49}}} to get {{{98}}}. 



{{{t = (-200 +- 592)/(98)}}} Take the square root of {{{350464}}} to get {{{592}}}. 



{{{t = (-200 + 592)/(98)}}} or {{{t = (-200 - 592)/(98)}}} Break up the expression. 



{{{t = (392)/(98)}}} or {{{t =  (-792)/(98)}}} Combine like terms. 



{{{t = 4}}} or {{{t = -396/49}}} Simplify. 



So the possible solutions are {{{t = 4}}} or {{{t = -396/49}}} 

  
  
However, since a negative time value doesn't make any sense, we must ignore the value {{{t = -396/49}}}



So the only solution is {{{t = 4}}}