Question 577538


{{{x^2-2x-3=5}}} Start with the given equation.



{{{x^2-2x-3-5=0}}} Subtract 5 from both sides.



{{{x^2-2x-8=0}}} Combine like terms.



Notice that the quadratic {{{x^2-2x-8}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=-2}}}, and {{{C=-8}}}



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



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



{{{x = (-(-2) +- sqrt( (-2)^2-4(1)(-8) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-2}}}, and {{{C=-8}}}



{{{x = (2 +- sqrt( (-2)^2-4(1)(-8) ))/(2(1))}}} Negate {{{-2}}} to get {{{2}}}. 



{{{x = (2 +- sqrt( 4-4(1)(-8) ))/(2(1))}}} Square {{{-2}}} to get {{{4}}}. 



{{{x = (2 +- sqrt( 4--32 ))/(2(1))}}} Multiply {{{4(1)(-8)}}} to get {{{-32}}}



{{{x = (2 +- sqrt( 4+32 ))/(2(1))}}} Rewrite {{{sqrt(4--32)}}} as {{{sqrt(4+32)}}}



{{{x = (2 +- sqrt( 36 ))/(2(1))}}} Add {{{4}}} to {{{32}}} to get {{{36}}}



{{{x = (2 +- sqrt( 36 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (2 +- 6)/(2)}}} Take the square root of {{{36}}} to get {{{6}}}. 



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



{{{x = (8)/(2)}}} or {{{x =  (-4)/(2)}}} Combine like terms. 



{{{x = 4}}} or {{{x = -2}}} Simplify. 



So the solutions are {{{x = 4}}} or {{{x = -2}}}