Solve
(3x-2)^2=2
(3x-2)^2=2
3x-2 = sqrt2
3x= sqrt2 + 2
x = (sqrt2 + 2) / 3
By taking only the positive root, you have lost a solution. The quadratic formula, applied to
9x2 - 12x + 4 = 2
reveals the other root: (2-√2)/3
To solve the equation (3x-2)^2=2, we need to isolate the variable x.
Step 1: Expand the equation
(3x-2)^2 = 2
(3x-2)(3x-2) = 2
Step 2: Apply the FOIL method to expand the left side of the equation
9x^2 - 6x - 6x + 4 = 2
9x^2 - 12x + 4 = 2
Step 3: Subtract 2 from both sides of the equation to have 0 on the right side
9x^2 - 12x + 4 - 2 = 0
9x^2 - 12x + 2 = 0
This equation is a quadratic equation in the form of ax^2 + bx + c, where
a = 9,
b = -12, and
c = 2.
Now, we can use the quadratic formula to solve for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values, we have:
x = (-(-12) ± √((-12)^2 - 4(9)(2))) / (2(9))
x = (12 ± √(144 - 72)) / 18
x = (12 ± √72) / 18
Simplifying further,
x = (12 ± 6√2) / 18
x = (2 ± √2) / 3
Therefore, the solutions for the equation (3x-2)^2 = 2 are x = (2 + √2) / 3 and x = (2 - √2) / 3.