Find intercepts of: 2x^2+2y^2-12x+8y-24=0

2x² + 2y² - 12x + 8y - 24 = 0

+ 24 + 24

2x² + 2y² - 12x + 8y = 24

2x² - 12x + 2y² + 8y = 24

2x² - 12x + 18 + 2y² + 8y + 4 = 24 + 18 + 8

2 (x²) - 2 (6x) + 2 (9) + 2 (y²) + 2 (4y) + 2 (2) = 50

2 (x² - 6x + 9) + 2 (y² + 4y + 4) = 50

2 (x² - 3x - 3x + 9) + 2 (y² + 2y + 2y + 4) = 50

2[x (x) - x (3) - 3 (x) + 3 (3) ] + 2[y (y) + y (2) + 2 (y) + 2 (2) ] = 50

2[x (x - 3) - 3 (x - 3) ] + 2[y (y + 2) + 2 (y + 2) ] = 50

2 (x - 3) (x - 3) + 2 (y + 2) (y + 2) = 50

2 (x - 3) ² + 2 (y + 2) ² = 50

2 2

(x - 3) ² + (y + 2) ² = 25

25 25 25

(x - 3) ²/25 + (y + 2) ²/25 = 1

X-Intercept: (x - 3) ²/25 + (y + 2) ²/25 = 1

(x - 3) ²/25 + (0 + 2) ²/25 = 1

(x - 3) ²/25 + (2) ²/25 = 1

⁽ˣ⁻³⁾ ²/₂₅ + ⁴/₂₅ = 1

- ⁴/₂₅ - ⁴/₂₅

⁽ˣ⁻³⁾ ²/₂₅ = ²¹/₂₅

25 ( ⁽ˣ⁻³⁾ ²/₂₅) = 25 (²¹/₂₅)

(x - 3) ² = 21

√ (x - 3) ² = ±√21

x - 3 = ±√21

+ 3 + 3

x = 3 ± √21

Y-Intercept: (x - 3) ²/25 + (y + 2) ²/25 = 1

(0 - 3) ²/25 + (y + 2) ²/25 = 1

(-3) ²/25 + (y + 2) ²/25 = 1

9/25 + (y + 2) ²/25 = 1

- 9/25 - 9/25

(y + 2) ²/25 = 16/25

25 ((y + 2) ²/25) = 25 (16/25)

(y + 2) ² = 16

√ (y + 2) ² = ±√16

y + 2 = ±4

- 2 - 2

y = - 2 ± 4

y = - 2 + 4 or y = - 2 - 4

y = 2 or y = - 6