Question 585217
I'll do the first one to get you started


# 1



{{{9x^2+10x-13=0}}} Start with the given equation.



Notice that the quadratic {{{9x^2+10x-13}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=9}}}, {{{B=10}}}, and {{{C=-13}}}



Let's use the quadratic formula to solve for "x":



{{{x = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{x = (-(10) +- sqrt( (10)^2-4(9)(-13) ))/(2(9))}}} Plug in  {{{A=9}}}, {{{B=10}}}, and {{{C=-13}}}



{{{x = (-10 +- sqrt( 100-4(9)(-13) ))/(2(9))}}} Square {{{10}}} to get {{{100}}}. 



{{{x = (-10 +- sqrt( 100--468 ))/(2(9))}}} Multiply {{{4(9)(-13)}}} to get {{{-468}}}



{{{x = (-10 +- sqrt( 100+468 ))/(2(9))}}} Rewrite {{{sqrt(100--468)}}} as {{{sqrt(100+468)}}}



{{{x = (-10 +- sqrt( 568 ))/(2(9))}}} Add {{{100}}} to {{{468}}} to get {{{568}}}



{{{x = (-10 +- sqrt( 568 ))/(18)}}} Multiply {{{2}}} and {{{9}}} to get {{{18}}}. 



{{{x = (-10 +- 2*sqrt(142))/(18)}}} 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 = (-10+2*sqrt(142))/(18)}}} or {{{x = (-10-2*sqrt(142))/(18)}}} Break up the expression.  



{{{x = (-5+sqrt(142))/(9)}}} or {{{x = (-5-sqrt(142))/(9)}}} Reduce 



So the solutions are {{{x = (-5+sqrt(142))/(9)}}} or {{{x = (-5-sqrt(142))/(9)}}} 

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# 2



{{{5y^2-8y=2}}} Start with the given equation.



{{{5y^2-8y-2=0}}} Subtract 2 from both sides.



Notice that the quadratic {{{5y^2-8y-2}}} is in the form of {{{Ay^2+By+C}}} where {{{A=5}}}, {{{B=-8}}}, and {{{C=-2}}}



Let's use the quadratic formula to solve for "y":



{{{y = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{y = (-(-8) +- sqrt( (-8)^2-4(5)(-2) ))/(2(5))}}} Plug in  {{{A=5}}}, {{{B=-8}}}, and {{{C=-2}}}



{{{y = (8 +- sqrt( (-8)^2-4(5)(-2) ))/(2(5))}}} Negate {{{-8}}} to get {{{8}}}. 



{{{y = (8 +- sqrt( 64-4(5)(-2) ))/(2(5))}}} Square {{{-8}}} to get {{{64}}}. 



{{{y = (8 +- sqrt( 64--40 ))/(2(5))}}} Multiply {{{4(5)(-2)}}} to get {{{-40}}}



{{{y = (8 +- sqrt( 64+40 ))/(2(5))}}} Rewrite {{{sqrt(64--40)}}} as {{{sqrt(64+40)}}}



{{{y = (8 +- sqrt( 104 ))/(2(5))}}} Add {{{64}}} to {{{40}}} to get {{{104}}}



{{{y = (8 +- sqrt( 104 ))/(10)}}} Multiply {{{2}}} and {{{5}}} to get {{{10}}}. 



{{{y = (8 +- 2*sqrt(26))/(10)}}} 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>)  



{{{y = (8+2*sqrt(26))/(10)}}} or {{{y = (8-2*sqrt(26))/(10)}}} Break up the expression.  



{{{y = (4+sqrt(26))/(5)}}} or {{{y = (4-sqrt(26))/(5)}}} Reduce



So the solutions are {{{y = (4+sqrt(26))/(5)}}} or {{{y = (4-sqrt(26))/(5)}}} 


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