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Algebra

Question 5 of 9

Factorising Quadratic Equations

Question

Factorise \((3r - 2)^2 = 36\)

Show solution Hide solution Fully worked — 4 steps
  1. Take the square root of both sides
    \[ (3r - 2)^2 = 36 \]

    Since \(\sqrt{36} = \pm 6\):

    \[ 3r - 2 = \pm 6 \]
  2. Add \(2\) to both sides
    \[ 3r = 2 \pm 6 \]
  3. Find the two solutions

    Then either

    \[ 3r = 2 + 6 \Rightarrow r = \frac{8}{3} \]

    or

    \[ 3r = 2 - 6 \Rightarrow r = \frac{-4}{3} \]
  4. State the solutions

    The solutions are \(r = \frac{8}{3}\) or \(r = \frac{-4}{3}\). That is, \(r\) is eight thirds and \(r\) is minus four thirds.