Question

Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42

Answer 1

Answer: x = 13 and x = 1

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Work Shown:

`(\text{x}-7)^2 = 36\\\\\sqrt{(\text{x}-7)^2} = √(36)\\\\\text{x}-7 = \pm√(36)\\\\\text{x}-7 = \pm6\\\\\text{x}-7 = 6 \ \text{ or } \ \text{x}-7 = -6\\\\\text{x} = 6+7 \ \text{ or } \ \text{x} = -6+7\\\\\text{x} = 13 \ \text{ or } \ \text{x} = 1\\\\`

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Check:

Plug in x = 13

`(\text{x}-7)^2 = 36\\\\(13-7)^2 = 36\\\\(6)^2 = 36\\\\36 = 36 \ \ \checkmark\\\\`

This confirms x = 13

Now check x = 1

`(\text{x}-7)^2 = 36\\\\(1-7)^2 = 36\\\\(-6)^2 = 36\\\\36 = 36 \ \ \checkmark\\\\`

The value x = 1 is confirmed as well.

Both solutions are confirmed.