Question 89126
Solve by using the quadratic formula. x^2 = –5x + 11 
:
Put it in the general form;  ax^2 + bx + c = 0
:
x^2 + 5x - 11 = 0
:
In this problem, a=1, b=5, c=-11
:
The quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
:
Substitute for a, b, and c, and you have:
{{{x = (-5 +- sqrt( 5^2 - (4 * 1* -11) ))/(2*1) }}}
:
{{{x = (-5 +- sqrt( 25 - (-44) ))/(2) }}} 
:
{{{x = (-5 +- sqrt( 25 + 44) )/(2) }}}; minus a minus is a plus
:
{{{x = (-5 +- sqrt( 69 ))/(2) }}}
:
1st solution:
{{{x = (-5 + 8.3066)/2}}}
:
{{{x = + 3.3066/2}}}
:
x = +1.6533   
:
2nd solution:
{{{x = (-5 - 8.3066)/2}}}
:
{{{x = -13.3066/2}}}
:
x = -6.6533
:
It's good idea to check solution by substitution in the original equation:
x^2 = -5x + 11
Substitute 1.6533 for x:
1.6533^2 = -5(1.6533) + 11
2.7334 = -8.2665 + 11
2.7334 ~ 2.7335
:
You can check the solution using the 2nd solution
:
Can you handle this now?