Question

1. 100 + (x - 2)² = 149

Explanation:

Step1: Isolate the squared term

Subtract 100 from both sides.
$$(x-2)^2 = 149 - 100$$
$$(x-2)^2 = 49$$

Step2: Take square roots of both sides

Solve for $x-2$ using square root property.
$$x-2 = \pm\sqrt{49}$$
$$x-2 = \pm7$$

Step3: Solve for x

Split into two cases and solve each.
Case 1: $x-2 = 7$
$$x = 7 + 2 = 9$$
Case 2: $x-2 = -7$
$$x = -7 + 2 = -5$$

Answer:

$x=9$ or $x=-5$