Question 148495
a)


{{{x^3-4x=0}}} Start with the given equation.



{{{x(x^2-4)=0}}} Factor out the GCF x



{{{x(x+2)(x-2)=0}}} Factor {{{x^2-4}}} to get {{{(x+2)(x-2)}}}



Now set each factor equal to zero:


{{{x=0}}}, {{{x+2=0}}} or {{{x-2=0}}}



Now solve for x for each factor:


{{{x=0}}}, {{{x=-2}}} or {{{x=2}}}



So the solutions of {{{x^3-4x=0}}} are {{{x=0}}}, {{{x=-2}}} or {{{x=2}}}




<hr>


b)


{{{2x^2+7x-15=0}}} Start with the given equation.



Let's use the quadratic formula to solve for x



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



{{{x = (-(7) +- sqrt( (7)^2-4(2)(-15) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=7}}}, and {{{c=-15}}}



{{{x = (-7 +- sqrt( 49-4(2)(-15) ))/(2(2))}}} Square {{{7}}} to get {{{49}}}. 



{{{x = (-7 +- sqrt( 49--120 ))/(2(2))}}} Multiply {{{4(2)(-15)}}} to get {{{-120}}}



{{{x = (-7 +- sqrt( 49+120 ))/(2(2))}}} Rewrite {{{sqrt(49--120)}}} as {{{sqrt(49+120)}}}



{{{x = (-7 +- sqrt( 169 ))/(2(2))}}} Add {{{49}}} to {{{120}}} to get {{{169}}}



{{{x = (-7 +- sqrt( 169 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{x = (-7 +- 13)/(4)}}} Take the square root of {{{169}}} to get {{{13}}}. 



{{{x = (-7 + 13)/(4)}}} or {{{x = (-7 - 13)/(4)}}} Break up the expression. 



{{{x = (6)/(4)}}} or {{{x =  (-20)/(4)}}} Combine like terms. 



{{{x = 3/2}}} or {{{x = -5}}} Simplify. 



So our answers are {{{x = 3/2}}} or {{{x = -5}}}