Firstly, we want to convert the equation into a more standard form by getting rid of the constant (4) that is multiplying the square. We do this by dividing both sides of the equation by 4:
4(x + 7)² = 11
(x + 7)² = 11 / 4
Now, it is time to take the square root of both sides of the equation. The square root of a squared term cancels the square, and remember that when you take the square root of a number you get two solutions: positive and negative.
So (x + 7) equals to sqrt(11 / 4) and -sqrt(11 / 4), respectively.
To solve for x, simply subtract 7 from both sides:
x = sqrt(11 / 4) - 7
This gives us the solution corresponding to the positive square root. In the case of the negative square root, the equation is:
x = -sqrt(11 / 4) - 7
Therefore, we have two solutions to the original equation:
The value of x1, when taking the positive root, is -5.3416876048223.
The value of x2, when taking the negative root, is -8.658312395177699.
So the solution set for the given equation is x1 = -5.3416876048223 and x2 = -8.658312395177699.