Question 282629
I'll do the first one to get you started.


{{{ -x^2=15x+30 }}} Start with the given equation.



{{{ 0=x^2+15x+30 }}} Add {{{x^2}}} to both sides



Notice that the quadratic {{{x^2+15x+30}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=15}}}, and {{{C=30}}}



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



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



{{{x = (-(15) +- sqrt( (15)^2-4(1)(30) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=15}}}, and {{{C=30}}}



{{{x = (-15 +- sqrt( 225-4(1)(30) ))/(2(1))}}} Square {{{15}}} to get {{{225}}}. 



{{{x = (-15 +- sqrt( 225-120 ))/(2(1))}}} Multiply {{{4(1)(30)}}} to get {{{120}}}



{{{x = (-15 +- sqrt( 105 ))/(2(1))}}} Subtract {{{120}}} from {{{225}}} to get {{{105}}}



{{{x = (-15 +- sqrt( 105 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-15+sqrt(105))/(2)}}} or {{{x = (-15-sqrt(105))/(2)}}} Break up the expression.  



So the solutions are {{{x = (-15+sqrt(105))/(2)}}} or {{{x = (-15-sqrt(105))/(2)}}}