Simplify the expression 125 - 5x2 as much as possible after substituting 5 sin (θ) for x. (Assume 0° < θ < 90°.)

125 - 5x² = 0 when x = 5 sin θ

⇒ 125 - 5 (5 sinθ) ²

⇒ 125 - 5 (25 sin²θ)

⇒ 125 - 125 sin²θ

⇒ 125 (1 - sin²θ)

⇒ 125 (1 - sinθ) (1 + sinθ) This is simplified

Solving for θ:

⇒ (1 - sinθ) (1 + sinθ) = 0

⇒ (1 - sinθ) = 0 (1 + sinθ) = 0

⇒ sinθ = 0 sinθ = - 1

θ = 0° θ = 180°

Since neither value satisifies 0° < θ < 90° there is no solution