Solve each quadratic equation by completing the square.
x^2-6x+2=0
http://www.purplemath.com/modules/sqrquad.htm
To solve the quadratic equation x^2 - 6x + 2 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 - 6x = -2
Step 2: Take half of the coefficient of x and square it:
(-6/2)^2 = (-3)^2 = 9
Step 3: Add the value obtained in step 2 to both sides of the equation:
x^2 - 6x + 9 = -2 + 9
x^2 - 6x + 9 = 7
Step 4: Factor the left side of the equation as a perfect square trinomial:
(x - 3)^2 = 7
Step 5: Take the square root of both sides of the equation:
√((x - 3)^2) = ±√7
|x - 3| = ±√7
Step 6: Set up two equations, one with a positive square root and one with a negative square root:
x - 3 = √7 or x - 3 = -√7
Step 7: Solve each equation separately:
For the first equation, add 3 to both sides:
x = 3 + √7
For the second equation, add 3 to both sides:
x = 3 - √7
So, the solutions to the quadratic equation x^2 - 6x + 2 = 0 by completing the square are x = 3 + √7 and x = 3 - √7.