Question 248346


{{{5d^2-10d=0}}} Start with the given equation



{{{5d(d-2)=0}}} Factor out the GCF 5d.



Now set each factor equal to zero:

{{{5d=0}}} or  {{{d-2=0}}} 


{{{d=0}}} or  {{{d=2}}}    Solve for d in each case



So our answers are 


 {{{d=0}}} or  {{{d=2}}}



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2) 


{{{8x^2 = 16}}} Start with the given equation.



{{{8x^2 - 16=0}}} Subtract 16 from both sides.



Notice that the quadratic {{{8x^2-16}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=8}}}, {{{B=0}}}, and {{{C=-16}}}



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



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



{{{x = (-(0) +- sqrt( (0)^2-4(8)(-16) ))/(2(8))}}} Plug in  {{{A=8}}}, {{{B=0}}}, and {{{C=-16}}}



{{{x = (-0 +- sqrt( 0-4(8)(-16) ))/(2(8))}}} Square {{{0}}} to get {{{0}}}. 



{{{x = (-0 +- sqrt( 0--512 ))/(2(8))}}} Multiply {{{4(8)(-16)}}} to get {{{-512}}}



{{{x = (-0 +- sqrt( 0+512 ))/(2(8))}}} Rewrite {{{sqrt(0--512)}}} as {{{sqrt(0+512)}}}



{{{x = (-0 +- sqrt( 512 ))/(2(8))}}} Add {{{0}}} to {{{512}}} to get {{{512}}}



{{{x = (-0 +- sqrt( 512 ))/(16)}}} Multiply {{{2}}} and {{{8}}} to get {{{16}}}. 



{{{x = (-0 +- 16*sqrt(2))/(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 = (-0)/(16) +- (16*sqrt(2))/(16)}}} Break up the fraction.  



{{{x = 0 +- sqrt(2)}}} Reduce.  



{{{x = sqrt(2)}}} or {{{x = -sqrt(2)}}} Break up the expression.  



So the solutions are {{{x = sqrt(2)}}} or {{{x = -sqrt(2)}}} 



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3) 




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



{{{3m^2-5m+2=0}}} Add 2 to both sides.



Notice that the quadratic {{{3m^2-5m+2}}} is in the form of {{{Am^2+Bm+C}}} where {{{A=3}}}, {{{B=-5}}}, and {{{C=2}}}



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



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



{{{m = (-(-5) +- sqrt( (-5)^2-4(3)(2) ))/(2(3))}}} Plug in  {{{A=3}}}, {{{B=-5}}}, and {{{C=2}}}



{{{m = (5 +- sqrt( (-5)^2-4(3)(2) ))/(2(3))}}} Negate {{{-5}}} to get {{{5}}}. 



{{{m = (5 +- sqrt( 25-4(3)(2) ))/(2(3))}}} Square {{{-5}}} to get {{{25}}}. 



{{{m = (5 +- sqrt( 25-24 ))/(2(3))}}} Multiply {{{4(3)(2)}}} to get {{{24}}}



{{{m = (5 +- sqrt( 1 ))/(2(3))}}} Subtract {{{24}}} from {{{25}}} to get {{{1}}}



{{{m = (5 +- sqrt( 1 ))/(6)}}} Multiply {{{2}}} and {{{3}}} to get {{{6}}}. 



{{{m = (5 +- 1)/(6)}}} Take the square root of {{{1}}} to get {{{1}}}. 



{{{m = (5 + 1)/(6)}}} or {{{m = (5 - 1)/(6)}}} Break up the expression. 



{{{m = (6)/(6)}}} or {{{m =  (4)/(6)}}} Combine like terms. 



{{{m = 1}}} or {{{m = 2/3}}} Simplify. 



So the solutions are {{{m = 1}}} or {{{m = 2/3}}}