Question 323283
# 1




{{{5x^2-x-6=0}}} Start with the given equation.



Notice that the quadratic {{{5x^2-x-6}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=5}}}, {{{B=-1}}}, 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 = (-(-1) +- sqrt( (-1)^2-4(5)(-6) ))/(2(5))}}} Plug in  {{{A=5}}}, {{{B=-1}}}, and {{{C=-6}}}



{{{x = (1 +- sqrt( (-1)^2-4(5)(-6) ))/(2(5))}}} Negate {{{-1}}} to get {{{1}}}. 



{{{x = (1 +- sqrt( 1-4(5)(-6) ))/(2(5))}}} Square {{{-1}}} to get {{{1}}}. 



{{{x = (1 +- sqrt( 1--120 ))/(2(5))}}} Multiply {{{4(5)(-6)}}} to get {{{-120}}}



{{{x = (1 +- sqrt( 1+120 ))/(2(5))}}} Rewrite {{{sqrt(1--120)}}} as {{{sqrt(1+120)}}}



{{{x = (1 +- sqrt( 121 ))/(2(5))}}} Add {{{1}}} to {{{120}}} to get {{{121}}}



{{{x = (1 +- sqrt( 121 ))/(10)}}} Multiply {{{2}}} and {{{5}}} to get {{{10}}}. 



{{{x = (1 +- 11)/(10)}}} Take the square root of {{{121}}} to get {{{11}}}. 



{{{x = (1 + 11)/(10)}}} or {{{x = (1 - 11)/(10)}}} Break up the expression. 



{{{x = (12)/(10)}}} or {{{x =  (-10)/(10)}}} Combine like terms. 



{{{x = 6/5}}} or {{{x = -1}}} Simplify. 



So the solutions are {{{x = 6/5}}} or {{{x = -1}}} 

  
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# 2



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



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



{{{0=x^2-2x+3}}} Add 3 to both sides.



{{{x^2-2x+3=0}}} Rearrange the equation.



Now the equation is in standard form {{{Ax^2+Bx+C=0}}}