Question

4(x - 1)(3x - 1) = 0 answer?

Answer 1

`x = 1 \ \ \ \text{OR} \ \ \ x = (1)/(3)`

Explanation:

First, multiply out the set of parentheses and simplify the resulting quadratic expression.

`4(x - 1)(3x - 1) = 0`

`4(3x^2-x-3x+1) = 0`

`4(3x^2-4x+1) = 0`

Then, factor out a 3 from the parentheses to get rid of the coefficient on the quadratic's first term.

`4(3(x^2-(4)/(3)x+(1)/(3))) = 0`

`12(x^2-(4)/(3)x+(1)/(3)) = 0`

Finally, complete the square.

`12\left(x^2-(4)/(3)x + \left((-(4)/(3))/(2)\right)^2\right) = 12\left(-(1)/(3)\right) + 12\left((-(4)/(3))/(2)\right)^2`

`12\left(x^2-(4)/(3)x + (4)/(9)\right) = -4 + (16)/(3)`

`12\left(x - (2)/(3)\right)^2 = (4)/(3)`

`\left(x - (2)/(3)\right)^2 = (1)/(9)`

↓ take the square root of both sides

`x - (2)/(3)\right = \pm \sqrt{(1)/(9)}`

`x = (2)/(3) \pm \sqrt{(1)/(9)}`

`x = (2)/(3) \pm(1)/(3)`

↓ split into two equations

`x = (2)/(3) + (1)/(3) \ \ \ \text{OR} \ \ \ x = (2)/(3) - (1)/(3)`

`\boxed{x = 1 \ \ \ \text{OR} \ \ \ x = (1)/(3)}`