Question 207735
{{{2w^2-8w-6=(w-1)^2}}} Start with the given equation.



{{{2w^2-8w-6=w^2-2w+1}}} FOIL



{{{2w^2-8w-6-1w^2+2w-1=0}}} Get every term to the left side.



{{{w^2-6w-7=0}}} Combine like terms.



Notice that the quadratic {{{w^2-6w-7}}} is in the form of {{{Aw^2+Bw+C}}} where {{{A=1}}}, {{{B=-6}}}, and {{{C=-7}}}



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



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



{{{w = (-(-6) +- sqrt( (-6)^2-4(1)(-7) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-6}}}, and {{{C=-7}}}



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



{{{w = (6 +- sqrt( 36-4(1)(-7) ))/(2(1))}}} Square {{{-6}}} to get {{{36}}}. 



{{{w = (6 +- sqrt( 36--28 ))/(2(1))}}} Multiply {{{4(1)(-7)}}} to get {{{-28}}}



{{{w = (6 +- sqrt( 36+28 ))/(2(1))}}} Rewrite {{{sqrt(36--28)}}} as {{{sqrt(36+28)}}}



{{{w = (6 +- sqrt( 64 ))/(2(1))}}} Add {{{36}}} to {{{28}}} to get {{{64}}}



{{{w = (6 +- sqrt( 64 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{w = (6 +- 8)/(2)}}} Take the square root of {{{64}}} to get {{{8}}}. 



{{{w = (6 + 8)/(2)}}} or {{{w = (6 - 8)/(2)}}} Break up the expression. 



{{{w = (14)/(2)}}} or {{{w =  (-2)/(2)}}} Combine like terms. 



{{{w = 7}}} or {{{w = -1}}} Simplify. 



So the solutions are {{{w = 7}}} or {{{w = -1}}}