Question 147239


{{{x^2-7x-1=-7}}} Start with the given equation.



{{{x^2-7x-1+7=0}}} Get all terms to the left side.



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



Notice we have a quadratic equation 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 our answers are {{{x = 6}}} or {{{x = 1}}}