Question

Solve (x–3)² =5.
a. x=−3±5
b. x=8 and x=−2
c. x=5±3
d. x=3±5

Answer 1

To solve (x–3)² = 5, one takes the square root of both sides and then adds 3 to each solution, resulting in x = 3 + √5 and x = 3 - √5.

Step-by-step explanation:

To solve the equation (x–3)² = 5, we first take the square root of both sides to eliminate the exponent on the left side, yielding x – 3 = ±√5. Next, we isolate x by adding 3 to both sides of the equation, resulting in x = 3 ± √5. The square root of 5 is an irrational number, so we leave it under the radical and get two possible solutions: x = 3 + √5 and x = 3 - √5.

Therefore, the correct answer is d. x = 3 ± √5, which represents two possible values for x.