Answer:
x = 5 and x= -11
Explanation:
This equation is a quadratic equation because the variable x is raised to the power of 2 so, there will be two values for x.
Also, a quadratic equation is the product of two linear functions and each functions are equated to zero as seen in the solution below.
(x +3)^2 +8 = 72
Expand the bracket
(x + 3)(x + 3) + 8 =72
x^2 +3x + 3x + 9 +8 =72
x^2 + 6x + 17 = 72
Subtract 72 from both sides
x^2 + 6x + 17 -72 = 72- 72
x^2 + 6x - 55 = 0
Now let's solve for both values of x
The two numbers that when multiplied gives -55 and when summed gives 6 are...
...Yes! 11 and 5
x^2 + 11x - 5x -55 = 0
x(x + 11)-5 (x + 11) =0
(x - 5) (x + 11) = 0
x - 5 = 0
x = 5
x + 11 = 0
x = -11