Question

Plz Help <3

Given the equation (x – 3)2 – 32 = 17 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:
I ALREADY KNOW THE ANSWER TO PART A. Its x=10, x=-4
I dont know part B. Why the equation has 2 solutions. Help please

Answer 1

Square root is essentially the opposite of squaring a number. You're looking for whatever was multiplied by itself to get the answer. While it is natural to look at the positive square root, a lot of people forget there is a negative square root as well. Your problem involved √49. We know that 7*7 is 49. We also know that (-7)(-7) is 49. That's where your two answers come in. When you come to the point of taking the square root you have

`√((x-3)^2)=√(49) \\x-3= 7 \text{ or } x-3=-7`. Thus, two answers.