Question 161945
I'll do the first two to get you started


1)


{{{(4x+2)(2x) = 32 }}} Start with the given equation



{{{8x^2+4x = 32 }}} Distribute



{{{8x^2+4x-32=0}}} Subtract 32 from both sides



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=8}}}, {{{b=4}}}, and {{{c=-32}}}



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(8)(-32) ))/(2(8))}}} Plug in  {{{a=8}}}, {{{b=4}}}, and {{{c=-32}}}



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



{{{x = (-4 +- sqrt( 16--1024 ))/(2(8))}}} Multiply {{{4(8)(-32)}}} to get {{{-1024}}}



{{{x = (-4 +- sqrt( 16+1024 ))/(2(8))}}} Rewrite {{{sqrt(16--1024)}}} as {{{sqrt(16+1024)}}}



{{{x = (-4 +- sqrt( 1040 ))/(2(8))}}} Add {{{16}}} to {{{1024}}} to get {{{1040}}}



{{{x = (-4 +- sqrt( 1040 ))/(16)}}} Multiply {{{2}}} and {{{8}}} to get {{{16}}}. 



{{{x = (-4 +- 4*sqrt(65))/(16)}}} 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 = (-4+4*sqrt(65))/(16)}}} or {{{x = (-4-4*sqrt(65))/(16)}}} Break up the expression.  



{{{x = (-1+sqrt(65))/(4)}}} or {{{x = (-1-sqrt(65))/(4)}}} Reduce



So the answers are {{{x = (-1+sqrt(65))/(4)}}} or {{{x = (-1-sqrt(65))/(4)}}}



which approximate to {{{x=1.766}}} or {{{x=-2.266}}} 





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2)


{{{(3x+2)(9x+3) = 81 }}} Start with the given equation



{{{27x^2+27x+6 = 81 }}} FOIL



{{{27x^2+27x+6-81=0}}} Subtract 81 from both sides



{{{27x^2+27x-75=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=27}}}, {{{b=27}}}, and {{{c=-75}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(27) +- sqrt( (27)^2-4(27)(-75) ))/(2(27))}}} Plug in  {{{a=27}}}, {{{b=27}}}, and {{{c=-75}}}



{{{x = (-27 +- sqrt( 729-4(27)(-75) ))/(2(27))}}} Square {{{27}}} to get {{{729}}}. 



{{{x = (-27 +- sqrt( 729--8100 ))/(2(27))}}} Multiply {{{4(27)(-75)}}} to get {{{-8100}}}



{{{x = (-27 +- sqrt( 729+8100 ))/(2(27))}}} Rewrite {{{sqrt(729--8100)}}} as {{{sqrt(729+8100)}}}



{{{x = (-27 +- sqrt( 8829 ))/(2(27))}}} Add {{{729}}} to {{{8100}}} to get {{{8829}}}



{{{x = (-27 +- sqrt( 8829 ))/(54)}}} Multiply {{{2}}} and {{{27}}} to get {{{54}}}. 



{{{x = (-27 +- 9*sqrt(109))/(54)}}} 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 = (-27+9*sqrt(109))/(54)}}} or {{{x = (-27-9*sqrt(109))/(54)}}} Break up the expression.  



So the answers are {{{x = (-27+9*sqrt(109))/(54)}}} or {{{x = (-27-9*sqrt(109))/(54)}}} 



which approximate to {{{x=1.24}}} or {{{x=-2.24}}}