Solve the equation-
e^x2+5x+6=1
***big hint: e^0=1
so, set x2+5x+6=0 and solve for x
e^(x^2 + 5x + 6) = 1.
e^0 = 1,
x^2 + 5x + 6 = 0.
(x + 2) (x + 3) = 0,
x + 2 = 0,
x = -2.
x + 3 = 0,
x = -3.
Solution set: x = -3, and x = -2.
To solve the equation e^(x^2+5x+6) = 1, you need to follow these steps:
Step 1: Subtract 1 from both sides of the equation to isolate the exponential term:
e^(x^2+5x+6) - 1 = 0
Step 2: Simplify the equation:
e^(x^2+5x+6) = e^0
e^(x^2+5x+6) = 1
Step 3: Notice that the exponential term on the left side is equal to 1. This means that the exponent itself must be equal to 0. Therefore, you can set the exponent equal to 0:
x^2 + 5x + 6 = 0
Step 4: Solve the quadratic equation. This equation can be factored into two binomial factors:
(x + 2)(x + 3) = 0
Step 5: Set each factor equal to zero and solve for x:
x + 2 = 0 or x + 3 = 0
Solving for x, we have two possible solutions:
x = -2 or x = -3
So, the solutions to the equation e^(x^2+5x+6) = 1 are x = -2 and x = -3.