Question 179509
# 1



{{{x^2-2x=15x-10}}} Start with the given equation.



{{{x^2-2x-15x+10=0}}} Get all terms to the left side.



{{{x^2-17x+10=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-17}}}, and {{{c=10}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-17) +- sqrt( (-17)^2-4(1)(10) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-17}}}, and {{{c=10}}}



{{{x = (17 +- sqrt( (-17)^2-4(1)(10) ))/(2(1))}}} Negate {{{-17}}} to get {{{17}}}. 



{{{x = (17 +- sqrt( 289-4(1)(10) ))/(2(1))}}} Square {{{-17}}} to get {{{289}}}. 



{{{x = (17 +- sqrt( 289-40 ))/(2(1))}}} Multiply {{{4(1)(10)}}} to get {{{40}}}



{{{x = (17 +- sqrt( 249 ))/(2(1))}}} Subtract {{{40}}} from {{{289}}} to get {{{249}}}



{{{x = (17 +- sqrt( 249 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (17+sqrt(249))/(2)}}} or {{{x = (17-sqrt(249))/(2)}}} Break up the expression.  



So the answers are {{{x = (17+sqrt(249))/(2)}}} or {{{x = (17-sqrt(249))/(2)}}} 



which approximate to {{{x=16.39}}} or {{{x=0.61}}} 



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# 2





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



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



{{{x^2-3x-8=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=-3}}}, 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 = (-(-3) +- sqrt( (-3)^2-4(1)(-8) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=-3}}}, and {{{c=-8}}}



{{{x = (3 +- sqrt( (-3)^2-4(1)(-8) ))/(2(1))}}} Negate {{{-3}}} to get {{{3}}}. 



{{{x = (3 +- sqrt( 9-4(1)(-8) ))/(2(1))}}} Square {{{-3}}} to get {{{9}}}. 



{{{x = (3 +- sqrt( 9--32 ))/(2(1))}}} Multiply {{{4(1)(-8)}}} to get {{{-32}}}



{{{x = (3 +- sqrt( 9+32 ))/(2(1))}}} Rewrite {{{sqrt(9--32)}}} as {{{sqrt(9+32)}}}



{{{x = (3 +- sqrt( 41 ))/(2(1))}}} Add {{{9}}} to {{{32}}} to get {{{41}}}



{{{x = (3 +- sqrt( 41 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (3+sqrt(41))/(2)}}} or {{{x = (3-sqrt(41))/(2)}}} Break up the expression.  



So the answers are {{{x = (3+sqrt(41))/(2)}}} or {{{x = (3-sqrt(41))/(2)}}} 



which approximate to {{{x=4.702}}} or {{{x=-1.702}}}