What are the solutions to the equation x^2 - 10x + 25 = 0?

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Question: What are the solutions to the equation x^2 - 10x + 25 = 0?

Options:

Correct Answer: x = 5

Solution:

The equation can be factored as (x - 5)(x - 5) = 0. Thus, the solution is x = 5 (a repeated root).

What are the solutions to the equation x^2 - 10x + 25 = 0?

What are the solutions to the equation x^2 - 10x + 25 = 0?

Step 1: Start with the equation x^2 - 10x + 25 = 0.
Step 2: Look for two numbers that multiply to 25 (the last number) and add up to -10 (the middle number).
Step 3: The numbers -5 and -5 work because -5 * -5 = 25 and -5 + -5 = -10.
Step 4: Rewrite the equation using these numbers: (x - 5)(x - 5) = 0.
Step 5: This can also be written as (x - 5)^2 = 0.
Step 6: To find the solution, set x - 5 = 0.
Step 7: Solve for x by adding 5 to both sides: x = 5.
Step 8: Since we factored it as (x - 5)(x - 5), this means x = 5 is a repeated root.

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