First, expand the square:
3(3x-1)^2 + 34 = 46
3(9x^2 - 6x + 1) + 34 = 46
27x^2 - 18x + 3 + 34 = 46
27x^2 - 18x + 37 = 46
Now, bring all terms to one side of the equation:
27x^2 - 18x + 37 - 46 = 0
27x^2 - 18x - 9 = 0
Divide by 9 to simplify:
3x^2 - 2x - 1 = 0
Now, we can use the quadratic formula to solve for x:
x = (-(-2) ± √((-2)^2 - 4*3*(-1))) / (2*3)
x = (2 ± √(4 + 12)) / 6
x = (2 ± √16) / 6
x = (2 ± 4) / 6
Therefore, the solutions for x are:
x = (2 + 4) / 6 = 6 / 6 = 1
x = (2 - 4) / 6 = -2 / 6 = -1/3
So, the solutions for x are x = 1 and x = -1/3.
Solve the following quadratic equation for all values of xx in simplest form.
3(3x−1)^2+34=46
1 answer