Question 151430
I'll do the first two to get you started.



# 1



{{{x^2-4x+8=0}}} Start with the given equation.



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



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



{{{x = (4 +- sqrt( 16-4(1)(8) ))/(2(1))}}} Square {{{-4}}} to get {{{16}}}. 



{{{x = (4 +- sqrt( 16-32 ))/(2(1))}}} Multiply {{{4(1)(8)}}} to get {{{32}}}



{{{x = (4 +- sqrt( -16 ))/(2(1))}}} Subtract {{{32}}} from {{{16}}} to get {{{-16}}}



{{{x = (4 +- sqrt( -16 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (4 +- 4*i)/(2)}}} Take the square root of {{{-16}}} to get {{{4*i}}}. 



{{{x = (4 + 4*i)/(2)}}} or {{{x = (4 - 4*i)/(2)}}} Break up the expression. 



{{{x = (4)/(2) + (4*i)/(2)}}} or {{{x =  (4)/(2) - (4*i)/(2)}}} Break up the fraction for each case. 



{{{x = 2+2*i}}} or {{{x =  2-2*i}}} Reduce. 



{{{x = 2+2*i}}} or {{{x = 2-2*i}}} Simplify. 



So our answers are {{{x = 2+2*i}}} or {{{x = 2-2*i}}} 

  


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# 2



{{{4x^2-6x-1=0}}} Start with the given equation.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=4}}}, {{{b=-6}}}, and {{{c=-1}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(-6) +- sqrt( (-6)^2-4(4)(-1) ))/(2(4))}}} Plug in  {{{a=4}}}, {{{b=-6}}}, and {{{c=-1}}}



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



{{{x = (6 +- sqrt( 36-4(4)(-1) ))/(2(4))}}} Square {{{-6}}} to get {{{36}}}. 



{{{x = (6 +- sqrt( 36--16 ))/(2(4))}}} Multiply {{{4(4)(-1)}}} to get {{{-16}}}



{{{x = (6 +- sqrt( 36+16 ))/(2(4))}}} Rewrite {{{sqrt(36--16)}}} as {{{sqrt(36+16)}}}



{{{x = (6 +- sqrt( 52 ))/(2(4))}}} Add {{{36}}} to {{{16}}} to get {{{52}}}



{{{x = (6 +- sqrt( 52 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{x = (6 +- 2*sqrt(13))/(8)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{x = (6+2*sqrt(13))/(8)}}} or {{{x = (6-2*sqrt(13))/(8)}}} Break up the expression.  



{{{x = (3+sqrt(13))/(4)}}} or {{{x = (4-sqrt(13))/(4)}}} Reduce.  



So the answers are {{{x = (3+sqrt(13))/(4)}}} or {{{x = (4-sqrt(13))/(4)}}}



which approximate to {{{x=1.651}}} or {{{x=-0.151}}}