Question 242758


{{{w^2-7w-18=0}}} Start with the given equation.



Notice that the quadratic {{{w^2-7w-18}}} is in the form of {{{Aw^2+Bw+C}}} where {{{A=1}}}, {{{B=-7}}}, and {{{C=-18}}}



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



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



{{{w = (-(-7) +- sqrt( (-7)^2-4(1)(-18) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-7}}}, and {{{C=-18}}}



{{{w = (7 +- sqrt( (-7)^2-4(1)(-18) ))/(2(1))}}} Negate {{{-7}}} to get {{{7}}}. 



{{{w = (7 +- sqrt( 49-4(1)(-18) ))/(2(1))}}} Square {{{-7}}} to get {{{49}}}. 



{{{w = (7 +- sqrt( 49--72 ))/(2(1))}}} Multiply {{{4(1)(-18)}}} to get {{{-72}}}



{{{w = (7 +- sqrt( 49+72 ))/(2(1))}}} Rewrite {{{sqrt(49--72)}}} as {{{sqrt(49+72)}}}



{{{w = (7 +- sqrt( 121 ))/(2(1))}}} Add {{{49}}} to {{{72}}} to get {{{121}}}



{{{w = (7 +- sqrt( 121 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{w = (7 +- 11)/(2)}}} Take the square root of {{{121}}} to get {{{11}}}. 



{{{w = (7 + 11)/(2)}}} or {{{w = (7 - 11)/(2)}}} Break up the expression. 



{{{w = (18)/(2)}}} or {{{w =  (-4)/(2)}}} Combine like terms. 



{{{w = 9}}} or {{{w = -2}}} Simplify. 



So the solutions are {{{w = 9}}} or {{{w = -2}}}