X² +5x +6=0
in some cases, yes.
If you want to factor it, which two factors of 6 add up to 5?
X^2 + 5x + 6 = 0; factorize
X^2 + 2x + 3x + 6 = 0.
X (x + 2) + 3(x + 2)= 0.
(X + 2) + (x + 3) = 0.
X + 2 = 0, x + 3 = 0.
Collect like terms.
X = -2, x = -3.
therefore, x = -2 or -3
To find the solutions for the quadratic equation x² + 5x + 6 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b² - 4ac)) / (2a)
In the given equation, a = 1, b = 5, and c = 6. We can substitute these values into the quadratic formula:
x = (-(5) ± √((5)² - 4(1)(6))) / (2(1))
Simplifying further:
x = (-5 ± √(25 - 24)) / 2
x = (-5 ± √1) / 2
Since the square root of 1 is 1:
x = (-5 ± 1) / 2
This gives us two possible solutions:
1. When we add 1 to -5 and divide the result by 2:
x = (-5 + 1) / 2
x = -4 / 2
x = -2
2. When we subtract 1 from -5 and divide the result by 2:
x = (-5 - 1) / 2
x = -6 / 2
x = -3
Therefore, the solutions to the equation x² + 5x + 6 = 0 are x = -2 and x = -3.