Factorising Quadratic Equations

Question

Factorise \((2y + 5)^2 = 49\)

Solution

Show solution Hide solution Fully worked — 4 steps

1. 1
   Take the square root of both sides

   \[ (2y + 5)^2 = 49 \]

   Since \(\sqrt{49} = \pm 7\):

   \[ 2y + 5 = \pm 7 \]
2. 2
   Add \(-5\) to both sides

   \[ 2y = -5 \pm 7 \]
3. 3
   Find the two solutions

   Then either

   \[ 2y = -5 + 7 \Rightarrow y = 1 \]

   or

   \[ 2y = -5 - 7 \Rightarrow y = -6 \]
4. State the solutions

   The solutions are \(y = 1\) or \(y = -6\). That is, \(y\) is one and \(y\) is minus six.