Expert: Bobby Soltani - 12/15/2005

Question
-x^+4x-1=0;       m^=2/3m+4/9




^=square
/=over (fraction)

Answer
Hi Diana,

-x^2 + 4x - 1 = 0
multiply everything through by -1 to get a positive sign on the x^2 term.

x^2 - 4x + 1 = 0
subtract 1 from both sides to get only the x^2 and x term on the left

x^2 - 4x = -1

take the coefficient of the x term (-4), and half it, then square it.  -4/2 = -2.  (-2)^2 = 4.  Add this to both sides of the equation.

x^2 - 4x + 4 = -1 + 4

convert the left hand side into squared form.

(x - 2)^2 = 3

solve by taking the square root of both sides.

x - 2 = +/- SQRT(3)

Separate the +/- into two equations.

x - 2 = SQRT(3)

x - 2 = -SQRT(3)

add 2 to both sides

x = SQRT(3) + 2 = 3.73
x = -SQRT(3) + 2 = 0.268

Do the same steps on the second problem to solve it.  Also, here are some examples at the following website.

http://www.purplemath.com/modules/sqrquad.htm

Let me know if you have any questions.

Bobby