Question 171818
{{{(x-6)^2 = 2x-9x + 38}}} Start with the given equation



{{{(x-6)^2 = -7x + 38}}} Combine like terms.



{{{x^2-12x+36 = -7x + 38}}} FOIL



{{{x^2-12x+36 +7x- 38=0}}} Subtract 7x from both sides. Add 38 to both sides.



{{{x^2-5x-2=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-5}}}, and {{{c=-2}}}



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(-5) +- sqrt( (-5)^2-4(1)(-2) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-5}}}, and {{{c=-2}}}



{{{x = (5 +- sqrt( (-5)^2-4(1)(-2) ))/(2(1))}}} Negate {{{-5}}} to get {{{5}}}. 



{{{x = (5 +- sqrt( 25-4(1)(-2) ))/(2(1))}}} Square {{{-5}}} to get {{{25}}}. 



{{{x = (5 +- sqrt( 25--8 ))/(2(1))}}} Multiply {{{4(1)(-2)}}} to get {{{-8}}}



{{{x = (5 +- sqrt( 25+8 ))/(2(1))}}} Rewrite {{{sqrt(25--8)}}} as {{{sqrt(25+8)}}}



{{{x = (5 +- sqrt( 33 ))/(2(1))}}} Add {{{25}}} to {{{8}}} to get {{{33}}}



{{{x = (5 +- sqrt( 33 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (5+sqrt(33))/(2)}}} or {{{x = (5-sqrt(33))/(2)}}} Break up the expression.  



So the answers are {{{x = (5+sqrt(33))/(2)}}} or {{{x = (5-sqrt(33))/(2)}}} 



which approximate to {{{x=5.372}}} or {{{x=-0.372}}}