Question 146762


{{{x^2+12x+36=64}}} Start with the given equation.



{{{x^2+12x+36-64=0}}} Get all terms to the left side.



{{{x^2+12x-28=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=1}}}, {{{b=12}}}, and {{{c=-28}}}



Let's use the quadratic formula to solve for x



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



{{{x = (-(12) +- sqrt( (12)^2-4(1)(-28) ))/(2(1))}}} Plug in  {{{a=1}}}, {{{b=12}}}, and {{{c=-28}}}



{{{x = (-12 +- sqrt( 144-4(1)(-28) ))/(2(1))}}} Square {{{12}}} to get {{{144}}}. 



{{{x = (-12 +- sqrt( 144--112 ))/(2(1))}}} Multiply {{{4(1)(-28)}}} to get {{{-112}}}



{{{x = (-12 +- sqrt( 144+112 ))/(2(1))}}} Rewrite {{{sqrt(144--112)}}} as {{{sqrt(144+112)}}}



{{{x = (-12 +- sqrt( 256 ))/(2(1))}}} Add {{{144}}} to {{{112}}} to get {{{256}}}



{{{x = (-12 +- sqrt( 256 ))/(2)}}} Multiply {{{2}}} and {{{1}}} to get {{{2}}}. 



{{{x = (-12 +- 16)/(2)}}} Take the square root of {{{256}}} to get {{{16}}}. 



{{{x = (-12 + 16)/(2)}}} or {{{x = (-12 - 16)/(2)}}} Break up the expression. 



{{{x = (4)/(2)}}} or {{{x =  (-28)/(2)}}} Combine like terms. 



{{{x = 2}}} or {{{x = -14}}} Simplify. 



So our answers are {{{x = 2}}} or {{{x = -14}}}