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
