Multiple choice

The solutions to the quadratic equation ${(x-1)}^{2}=\dfrac{4}{9}$ are

  1. $x=-\cfrac{5}{3}, x=\cfrac{5}{3}$
  2. $x=\cfrac{1}{3}, x=\cfrac{5}{3}$
  3. $x=\cfrac{5}{9}, x=\cfrac{13}{9}$
  4. $x=1\pm \sqrt{\cfrac{2}{3}}$
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B Correct answer
Explanation

(x-1)^2 = 4/9. Taking the square root of both sides: x-1 = +/- 2/3. x = 1 + 2/3 = 5/3 or x = 1 - 2/3 = 1/3.

AI explanation

To solve the equation, take the square root of both sides, remembering to include both the positive and negative roots, which gives x minus 1 equals positive two-thirds or negative two-thirds. For the positive case, adding 1 to two-thirds gives a solution of x equals five-thirds. For the negative case, adding 1 to negative two-thirds gives a solution of x equals one-third.

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