Question 176652
Is the equation {{{x^2+(13/2)x-13=0}}} ???



{{{x^2+(13/2)x-13=0}}} Start with the given equation.



{{{2x^2+13x-26=0}}} Multiply EVERY term by the LCD 2 to clear the fraction.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=2}}}, {{{b=13}}}, and {{{c=-26}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(13) +- sqrt( (13)^2-4(2)(-26) ))/(2(2))}}} Plug in  {{{a=2}}}, {{{b=13}}}, and {{{c=-26}}}



{{{x = (-13 +- sqrt( 169-4(2)(-26) ))/(2(2))}}} Square {{{13}}} to get {{{169}}}. 



{{{x = (-13 +- sqrt( 169--208 ))/(2(2))}}} Multiply {{{4(2)(-26)}}} to get {{{-208}}}



{{{x = (-13 +- sqrt( 169+208 ))/(2(2))}}} Rewrite {{{sqrt(169--208)}}} as {{{sqrt(169+208)}}}



{{{x = (-13 +- sqrt( 377 ))/(2(2))}}} Add {{{169}}} to {{{208}}} to get {{{377}}}



{{{x = (-13 +- sqrt( 377 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{x = (-13+sqrt(377))/(4)}}} or {{{x = (-13-sqrt(377))/(4)}}} Break up the expression.  



So the answers are {{{x = (-13+sqrt(377))/(4)}}} or {{{x = (-13-sqrt(377))/(4)}}} 



which approximate to {{{x=1.604}}} or {{{x=-8.104}}}