Question 183465
{{{(x - 3)^2 + (x + 2)^2 = 17}}} Start with the given equation.



{{{x^2-6x+9+x^2+4x+4 = 17}}} FOIL



{{{x^2-6x+9+x^2+4x+4 - 17=0}}} Subtract 17 from both sides.



{{{2x^2-2x-4=0}}} Combine like terms.



Notice we have a quadratic equation in the form of {{{ax^2+bx+c}}} where {{{a=2}}}, {{{b=-2}}}, and {{{c=-4}}}



Let's use the quadratic formula to solve for x



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



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



{{{x = (2 +- sqrt( (-2)^2-4(2)(-4) ))/(2(2))}}} Negate {{{-2}}} to get {{{2}}}. 



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



{{{x = (2 +- sqrt( 4--32 ))/(2(2))}}} Multiply {{{4(2)(-4)}}} to get {{{-32}}}



{{{x = (2 +- sqrt( 4+32 ))/(2(2))}}} Rewrite {{{sqrt(4--32)}}} as {{{sqrt(4+32)}}}



{{{x = (2 +- sqrt( 36 ))/(2(2))}}} Add {{{4}}} to {{{32}}} to get {{{36}}}



{{{x = (2 +- sqrt( 36 ))/(4)}}} Multiply {{{2}}} and {{{2}}} to get {{{4}}}. 



{{{x = (2 +- 6)/(4)}}} Take the square root of {{{36}}} to get {{{6}}}. 



{{{x = (2 + 6)/(4)}}} or {{{x = (2 - 6)/(4)}}} Break up the expression. 



{{{x = (8)/(4)}}} or {{{x =  (-4)/(4)}}} Combine like terms. 



{{{x = 2}}} or {{{x = -1}}} Simplify. 



So the answers are {{{x = 2}}} or {{{x = -1}}}