Solve and please explain how you arrived at your ans: square of 3x-1=2
are you asking to solve for (3x -1 ) squared= 2 ?
if so then just use foil or box technique to multiply (3x -1) against itself to get
9x^2 -6x +1 = 2
subtract 2 from both side to get
9x^2 - 6x -1 = 0
and then use quadratic formula to solve for x because i don't think you can factor this unless missing something
or, with less work,
(3x-1)^2 = 2
3x-1 = ±√2
3x = 1±√2
x = (1±√2)/3
To solve for the equation (3x - 1)² = 2, we need to follow a few steps. I'll explain each step as we go along.
Step 1: Expand the equation
To get rid of the square, we need to expand the left side of the equation using the formula (a - b)² = a² - 2ab + b².
(3x - 1)² = 2
(3x - 1)(3x - 1) = 2
9x² - 6x + 1 = 2
Step 2: Simplify the equation
The equation is now simplified by multiplying the terms in the brackets.
9x² - 6x + 1 = 2
Step 3: Move everything to one side
To solve for x, we need to move all the terms to one side of the equation, making it equal to zero. In this case, we subtract 2 from both sides.
9x² - 6x - 1 = 0
Now, we have a quadratic equation in standard form.
Step 4: Solve the quadratic equation
To solve the quadratic equation, we can either factor it, complete the square, or use the quadratic formula. In this case, factoring is not straightforward, so I'll use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
For our quadratic equation 9x² - 6x - 1 = 0, the coefficients are:
a = 9
b = -6
c = -1
Using the quadratic formula, we substitute these values:
x = (-(-6) ± √((-6)² - 4(9)(-1))) / (2(9))
x = (6 ± √(36 + 36)) / 18
x = (6 ± √(72)) / 18
Step 5: Simplify the expression
Let's simplify the expression further:
x = (6 ± √(8 × 9)) / 18
x = (6 ± 3√2) / 18
Step 6: Reduce the fraction
Now, let's simplify the fraction by dividing the numerator and denominator by 3:
x = 2/6 ± (1/2)√2
x = 1/3 ± (1/2)√2
Therefore, the solution to the equation (3x - 1)² = 2 is:
x = 1/3 + (1/2)√2
or
x = 1/3 - (1/2)√2