Question 686003
Step One: set the equation equal to 0
{{{x^2-10x + 25 - 12 = 0}}}
so,
{{{x^2 - 10x + 13 = 0}}}
apply the quadratic formula {{{x=(-b+-sqrt(b^2-4(a)(c)))/(2*a)}}}
compare to the standard equation ax^2 + bx + c = 0 and
a = 1, b = -10 and c = 13
therefore,
{{{x = (-(-10)+-sqrt((-10)^2-4(1)(13)))/(2*1)}}}
...
{{{x = (10+-sqrt(100-52))/2}}}
...
{{{x = (10+-sqrt(48))/2}}} where {{{sqrt(48) = sqrt(16*3) = 4sqrt(3)}}}
...
{{{x = (10+-4sqrt(3))/2}}}
...
{{{x = 10/2 +- 4sqrt(3)/2}}}
...
{{{x = 5 +- 2sqrt(3)}}}
ultimately
{{{highlight_green(x = 5 + 2sqrt(3))}}}
AND
{{{highlight_green(x = 5 - 2sqrt(3))}}}
..............................
Have more questions?
HomeworkHelpers@ReadingBoosters.com.
Delighted to help!
-Reading Boosters
Website: www.MyHomeworkAnswers.com