Solving Quadratic Equations

To solve x² + 6x + 5 = 0, factor it as (x + 1)(x + 5) = 0. Setting each factor to zero gives x = -1 and x = -5. Thus, the correct answer is x = -1 or x = -5.

To solve x² + 8x - 9 = 0, use the quadratic formula x = (-b ± √(b²-4ac))/2a. Here, a=1, b=8, c=-9. This gives x = 1 and x = -9, making the correct choice x = 1, x = -9.

To solve x² - 6x + 9 = 0, factor it as (x - 3)² = 0. Setting (x - 3) = 0 gives x = 3. Thus, the correct answer is x = 3.

To solve x² + 4x - 7 = 0, use the quadratic formula x = (-b ± √(b²-4ac))/2a. Here, a=1, b=4, c=-7. This gives x = -4/2 ± √(16+28)/2 = -2 ± √11. Thus, the correct answer is x = -2 ± √11.

To solve x² - 5x - 24 = 0, we can factor it as (x - 8)(x + 3) = 0. Setting each factor to zero gives x = 8 or x = -3, confirming the correct choice.

To solve x² - 8x + 15 = 0, factor it as (x - 3)(x - 5) = 0. Setting each factor to zero gives x = 3 or x = 5, which matches the correct answer choice.

To solve 4x² - 4x + 17 = 0, we use the quadratic formula x = (-b ± √(b² - 4ac)) / 2a. Here, a=4, b=-4, c=17. The discriminant (b² - 4ac) is negative, yielding complex roots: x = 1 ± 2i.

To solve 9x² - 12x + 13 = 0, we use the quadratic formula x = (-b ± √(b²-4ac)) / 2a. Here, a=9, b=-12, c=13. The discriminant (b²-4ac) is negative, leading to complex roots: x = 2/3 ± i√2/3.

To find the roots of 4x² - 4x + 5 = 0, use the quadratic formula x = (-b ± √(b²-4ac))/(2a). Here, a=4, b=-4, c=5. The discriminant (b²-4ac) is negative, yielding complex roots: x = 1 ± 2i.

To solve 4x² - 8x + 1 = 0, use the quadratic formula x = (-b ± √(b²-4ac))/(2a). Here, a=4, b=-8, c=1. This gives x = 2 ± √(16-4)/4 = 2 ± √12/4 = 2 ± √(4*3)/4 = 2 ± √3/2. The correct choice is x = 1 ± √2/2.