These are quadratic equations. Let's solve each one separately.
4x² + 5x - 6 = 0 To solve this, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a) Here, a = 4, b = 5, and c = -6 Plugging in these values, we get: x = (-5 ± √(5² - 44(-6))) / (2*4) x = (-5 ± √(25 + 96)) / 8 x = (-5 ± √121) / 8 x = (-5 ± 11) / 8 x = (-5 + 11) / 8 or x = (-5 - 11) / 8 x = 6 / 8 or x = -16 / 8 x = 3/4 or x = -2 So, the solutions are x = 3/4 and x = -2
4x² - 2x + 0.25 = 0 This equation can be factored as (2x - 0.5)² = 0 Solving for x, we get: 2x - 0.5 = 0 2x = 0.5 x = 0.25 So, the solution is x = 0.25
3x² + 4x + 5 = 0 To solve this, we can use the quadratic formula: a = 3, b = 4, c = 5 x = (-4 ± √(4² - 435)) / (2*3) x = (-4 ± √(16 - 60)) / 6 x = (-4 ± √(-44)) / 6 As the discriminant is negative, the solutions are complex numbers. x = (-4 ± 2√11 i) / 6 x = -2/3 ± √11/3 i So, the solutions are x = -2/3 + √11/3 i and x = -2/3 - √11/3 i
These are quadratic equations. Let's solve each one separately.
4x² + 5x - 6 = 0
To solve this, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a)
Here, a = 4, b = 5, and c = -6
Plugging in these values, we get:
x = (-5 ± √(5² - 44(-6))) / (2*4)
x = (-5 ± √(25 + 96)) / 8
x = (-5 ± √121) / 8
x = (-5 ± 11) / 8
x = (-5 + 11) / 8 or x = (-5 - 11) / 8
x = 6 / 8 or x = -16 / 8
x = 3/4 or x = -2
So, the solutions are x = 3/4 and x = -2
4x² - 2x + 0.25 = 0
This equation can be factored as (2x - 0.5)² = 0
Solving for x, we get:
2x - 0.5 = 0
2x = 0.5
x = 0.25
So, the solution is x = 0.25
3x² + 4x + 5 = 0
To solve this, we can use the quadratic formula:
a = 3, b = 4, c = 5
x = (-4 ± √(4² - 435)) / (2*3)
x = (-4 ± √(16 - 60)) / 6
x = (-4 ± √(-44)) / 6
As the discriminant is negative, the solutions are complex numbers.
x = (-4 ± 2√11 i) / 6
x = -2/3 ± √11/3 i
So, the solutions are x = -2/3 + √11/3 i and x = -2/3 - √11/3 i