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Q1 Solve the following quadratic equation using square roots: (x-5)2= 49

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To solve the quadratic equation \((x - 5)^2 = 49\) using square roots, follow these steps:

  1. Take the square root of both sides of the equation. Remember to consider both the positive and negative roots:

\[ x - 5 = \pm 7 \]

  1. Now you will have two separate equations to solve:

    a) \(x - 5 = 7\)

    b) \(x - 5 = -7\)

  2. Solve each equation:

    a) For \(x - 5 = 7\): \[ x = 7 + 5 = 12 \]

    b) For \(x - 5 = -7\): \[ x = -7 + 5 = -2 \]

  3. The solutions to the equation \((x - 5)^2 = 49\) are: \[ x = 12 \quad \text{and} \quad x = -2 \]