Please please please hel 1.) Explain why the equation (x-3)2 - 40=9 has two solutions. Then, solve the equation to find the
solutions. Show your work

x = 6 , x = -4 are the 2 solutions for the given equation

Step-by-step explanation:

Step 1 :

Given equation = (x-3)² - 40=9

Simplify this equation by expanding (x-3)² using the identity

(x-y)² = x² + y² - 2xy

here x = x and y = 3

Substituting we have,

x² + 9 -6x -40 = 9

=> x²-6x-40 = 9-9

=>  x²-6x-40 = 0

Step 2:

We can see that the above simplified equation is quadratic equation as the power of x is 2

When we solve for x, we will get 2 values for x , which means this equation  is true for 2 values of x. Hence this equation has 2 solutions.

Step 3 :

Solving for x²-6x-40 = 0

=> (x-6)(x+4) = 0

=> x-6 = 0    x +4 = 0

=> x = 6 , x = -4

Step 4 :

Answer :

x = 6 , x = -4 are the 2 solutions for the given equation

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)