Question

1. Given the equation (x – 3)2 – 32 = 17 a)

a) Solve the equation using the square root property to find the solutions. Show your work and round your final answer to the nearest tenth.

b) Explain why the given equation has two solutions.

Answer 1

we know that

The square root property is one method that is used to find the solutions to a quadratic equation.  This method involves taking the square roots of both sides of the equation.  
(x – 3)² – 32 = 17-------> (x – 3)² = 17+32-----------> (x – 3)² = 49
(x – 3)² = 7²--------> will take the square root of each side
so
√(x – 3)²=(+-)√7²------> notice the use of the  sign (+-), this will give us both a positive and  a negative root

then

x-3=7--------> x=10
x-3=-7-------> x=-4

the answer Part a) is
x=10
x=-4

Part b) Explain why the given equation has two solutions.

the answer part b) is
Because exist the possibility of two roots for every square root, one positive and one negative