Solving the Equation: 3(x+1)^2=108
In this article, we will go through the step-by-step solution to solve the equation 3(x+1)^2=108.
Step 1: Expand the Square
The first step is to expand the square in the equation using the formula (a+b)^2 = a^2 + 2ab + b^2.
3(x+1)^2 = 3(x^2 + 2x + 1) = 3x^2 + 6x + 3
So, the equation becomes:
3x^2 + 6x + 3 = 108
Step 2: Move all Terms to the Left Side
Our goal is to isolate the variable x. To do this, we will move all the terms to the left side of the equation.
3x^2 + 6x + 3 - 108 = 0
This simplifies to:
3x^2 + 6x - 105 = 0
Step 3: Factor the Quadratic Expression
Now, we need to factor the quadratic expression. After factoring, we get:
(3x + 21)(x - 5) = 0
Step 4: Solve for x
We have two possible solutions:
3x + 21 = 0 or x - 5 = 0
Case 1: 3x + 21 = 0
Subtract 21 from both sides:
3x = -21
Divide by 3:
x = -21/3 x = -7
Case 2: x - 5 = 0
Add 5 to both sides:
x = 5
Therefore, the solutions to the equation 3(x+1)^2=108 are x = -7 and x = 5.
I hope this step-by-step solution helps you understand how to solve the equation 3(x+1)^2=108.
