Question 467379
Solving for y:



{{{x=y^2-14y+25}}} Start with the given equation.



{{{0=y^2-14y+25-x}}} Subtract x from both sides.




Notice that the quadratic {{{y^2-14y+25-x}}} is in the form of {{{Ay^2+By+C}}} where {{{A=1}}}, {{{B=-14}}}, and {{{C=25-x}}} (note: x is a constant at this point)




Use quadratic formula

{{{y = (-B+-sqrt(B^2-4AC))/(2A)}}}



{{{y = (-(-14) +- sqrt( (-14)^2-4(1)(25-x) ))/(2(1))}}} Plug in  {{{A=1}}}, {{{B=-14}}}, and {{{C=25-x}}}



{{{y = (14 +- sqrt( (-14)^2-4(1)(25-x) ))/(2(1))}}} Negate {{{-14}}} to get {{{14}}}. 



{{{y = (14 +- sqrt( 196-4(1)(25-x) ))/(2(1))}}} Square {{{-14}}} to get {{{196}}}. 



{{{y = (14 +- sqrt( 196-4(25-x) ))/(2)}}} Multiply



{{{y = (14 +- sqrt( 4(49-(25-x)) ))/(2)}}} Factor out the GCF 4



{{{y = (14 +- sqrt( 4 )* sqrt((49-(25-x)) ))/(2)}}} Break up the square root.



{{{y = (14 +- 2* sqrt(49-25+x ))/(2)}}} Simplify



{{{y = (14 +- 2* sqrt(x+24))/(2)}}} Combine like terms and rearrange the terms.



{{{y = 7 +- sqrt(x+24)}}} Reduce.



So the solution is {{{y = 7 +- sqrt(x+24)}}} 



This is the same as saying that


{{{y = 7 + sqrt(x+24)}}}  or {{{y = 7 - sqrt(x+24)}}}