The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.
What is the quadratic equation behind two circular sections of equal area?
Herein we have two circular sections of equal area, whose expressions are described by the following geometric equations:
Semicircle
A = 0.5π · x² (1)
Half Semicircle
A = 0.25π · (x + 2)² (2)
By equalizing (1) and (2):
0.5π · x² = 0.25π · (x + 2)²
2 · x² = (x + 2)²
2 · x² = x² + 4 · x + 4
x² - 4 · x - 4 = 0
x² - 4 · x + 4 = 8
(x - 2)² = 8
x - 2 = ±√8
x = 2 ± √8
x = 2 ± 2√2
x = 2 · (1 ± √2)
x = 2 · (1 ± 1.41)
x₁ = 2 · 2.41 ∨ x₂ = 2 · (- 0.41)
x₁ = 4.82 ∨ x₂ = - 0.82
The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.
To learn more on quadratic equations: https://brainly.com/question/17177510
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