Question 155287
Solve for x:
{{{(x-6)^2+(51-x)^2 = 9}}} Simplify.
{{{(x^2-12x+36)+(2601-102x+x^2) = 9}}} Combine like-terms.
{{{2x^2-114x+2637 = 9}}} Subtract 9 from both sides.
{{{2x^2-114x+2628 = 0}}} Factor out a 2.
{{{2(x^2-57x+1314) = 0}}}, so...
{{{x^2-57x+1314 = 0}}} Use the quadratic formula:{{{x = (-b+-sqrt(b^2-4ac))/2a}}} Here, a = 1, b = -57, and c = 1314
{{{x = (-(-57)+-sqrt((-57)^2-4(1)(1314)))/2(1)}}} Simplify.
{{{x = (57+-sqrt(3249-5256))/2}}}
{{{x = (57+-sqrt(-2007))/2}}}
{{{x = (57+3sqrt(-223))/2}}} or {{{x = (57-3sqrt(-223))/2}}}
If you need the approximate answers, take the square roots as indicated:
{{{x = 28.5+22.4i}}} or {{{x = 28.5-22.4i}}}