2w^2+5w+3=0
2w^2+5w+3=0
2w^2+2w+3w+3=0
2w(w+1)+3(w+1)=0
(2w+3)+(w+1)=0
2w+3=0 w+1=0
2w=-3 w=-1
w=-3/2
To make it clearer,
2w^2 + 5w + 3 = 0
This factors into:
(2w + 3)(w + 1) = 0 (The + sign in the previous answer is a typo)
The rest is correct.
To solve the equation 2w^2 + 5w + 3 = 0, we can use the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / 2a
In this equation, a = 2, b = 5, and c = 3.
Plugging these values into the quadratic formula, we get:
w = (-5 ± √(5^2 - 4(2)(3))) / (2(2))
Simplifying further:
w = (-5 ± √(25 - 24)) / 4
w = (-5 ± √1) / 4
Since the square root of 1 is either 1 or -1, we have two possible solutions:
w = (-5 + 1) / 4 = -4/4 = -1
w = (-5 - 1) / 4 = -6/4 = -3/2
Therefore, the solutions to the equation 2w^2 + 5w + 3 = 0 are w = -1 and w = -3/2.