(x+3)²+8=72 (quadratic equation)
Please explain why this equation has 2 solutions and solve for both. I really appreciate it!

x = 5 or x = -11

Step-by-step explanation:

(x+3)²+8=72

x² + 6x + 9 + 8 = 72

x² + 6x -55 = 0

(x - 5) (x + 11) = 0

x = 5 or x = -11

x = 5 and x= -11

Step-by-step 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

step-by-step explanation: