Answer:
3(x + 2)^2 = 48 are x = 2 and x = -6
Explanation:
To solve the equation 3(x + 2)^2 = 48, we can follow these steps:
Expand the square by multiplying (x + 2) by itself: (x + 2) * (x + 2).
Simplify the expanded equation: 3(x^2 + 4x + 4) = 48.
Distribute the 3 to each term inside the parentheses: 3x^2 + 12x + 12 = 48.
Move all terms to one side of the equation by subtracting 48 from both sides: 3x^2 + 12x + 12 - 48 = 0.
Simplify the equation: 3x^2 + 12x - 36 = 0.
Divide the entire equation by 3 to simplify it further: x^2 + 4x - 12 = 0.
To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula.
Factoring: Factor the quadratic equation into two binomials: (x - 2)(x + 6) = 0.
Setting each factor to zero gives us two possible solutions: x - 2 = 0 or x + 6 = 0.
Solve for x: x = 2 or x = -6.
Therefore, the solutions to the equation 3(x + 2)^2 = 48 are x = 2 and x = -6.