Question 336187
{{{x(x+5)=14}}} Start with the given equation.



{{{x^2+5x=14}}} Distribute



{{{x^2+5x-14=0}}} Subtract 14 from both sides.



Notice that the quadratic {{{x^2+5x-14}}} is in the form of {{{Ax^2+Bx+C}}} where {{{A=1}}}, {{{B=5}}}, and {{{C=-14}}}



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



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



{{{x = (-(5) +- sqrt( (5)^2-4(1)(-14) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=5}}}, and {{{C=-14}}}



{{{x = (-5 +- sqrt( 25-4(1)(-14) ))/(2(1))}}} Square {{{5}}} to get {{{25}}}. 



{{{x = (-5 +- sqrt( 25--56 ))/(2(1))}}} Multiply {{{4(1)(-14)}}} to get {{{-56}}}



{{{x = (-5 +- sqrt( 25+56 ))/(2(1))}}} Rewrite {{{sqrt(25--56)}}} as {{{sqrt(25+56)}}}



{{{x = (-5 +- sqrt( 81 ))/(2(1))}}} Add {{{25}}} to {{{56}}} to get {{{81}}}



{{{x = (-5 +- sqrt( 81 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-5 +- 9)/(2)}}} Take the square root of {{{81}}} to get {{{9}}}. 



{{{x = (-5 + 9)/(2)}}} or {{{x = (-5 - 9)/(2)}}} Break up the expression. 



{{{x = (4)/(2)}}} or {{{x =  (-14)/(2)}}} Combine like terms. 



{{{x = 2}}} or {{{x = -7}}} Simplify. 



So the solutions are {{{x = 2}}} or {{{x = -7}}} 



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Jim