Solve
(2s + 5)(s + 1)= -1
mutltiply the left side, add one to each side, then refactor the left side.
I'm I on the right track?
2s^2 + 2s + 5s + 5 = -1
2s^2 + 7s + 5 = -1
2s^2 + 7s = -6
where do i go from here?
To solve the equation (2s + 5)(s + 1) = -1, we can follow these steps:
Step 1: Expand the equation
Expanding the equation means multiplying the terms inside the parentheses and simplifying.
First, multiply the terms using the Distributive Property:
(2s + 5)(s + 1) = 2s^2 + 2s + 5s + 5
Combining like terms:
2s^2 + 7s + 5 = -1
Step 2: Move all the terms to one side of the equation
Rearrange the equation so that all terms are on one side and the right side is equal to zero:
2s^2 + 7s + 5 + 1 = 0
2s^2 + 7s + 6 = 0
Step 3: Solve the quadratic equation
The equation now takes the form of a quadratic equation: as^2 + bs + c = 0. We can solve it by factoring, completing the square, or using the quadratic formula.
In this case, we can factor the equation:
2s^2 + 7s + 6 = (2s + 3)(s + 2) = 0
Set each factor equal to zero and solve for s:
2s + 3 = 0 or s + 2 = 0
For 2s + 3 = 0:
2s = -3
s = -3/2
For s + 2 = 0:
s = -2
So the solutions to the equation (2s + 5)(s + 1) = -1 are s = -3/2 and s = -2.