Question 550663
{{{x^2-7x=-6}}} Start with the given equation.



{{{x^2-7x+6=0}}} Add 6 to both sides.



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



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



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



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



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



{{{x = (7 +- sqrt( 49-4(1)(6) ))/(2(1))}}} Square {{{-7}}} to get {{{49}}}. 



{{{x = (7 +- sqrt( 49-24 ))/(2(1))}}} Multiply {{{4(1)(6)}}} to get {{{24}}}



{{{x = (7 +- sqrt( 25 ))/(2(1))}}} Subtract {{{24}}} from {{{49}}} to get {{{25}}}



{{{x = (7 +- sqrt( 25 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (7 +- 5)/(2)}}} Take the square root of {{{25}}} to get {{{5}}}. 



{{{x = (7 + 5)/(2)}}} or {{{x = (7 - 5)/(2)}}} Break up the expression. 



{{{x = (12)/(2)}}} or {{{x =  (2)/(2)}}} Combine like terms. 



{{{x = 6}}} or {{{x = 1}}} Simplify. 



So the solutions are {{{x = 6}}} or {{{x = 1}}}