If the quadratic equation x^2 - 10x + 25 = 0 is solved, what is the value of x?

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Question: If the quadratic equation x^2 - 10x + 25 = 0 is solved, what is the value of x? (2022)

Options:

Correct Answer: 5

Exam Year: 2022

Solution:

The equation can be factored as (x - 5)^2 = 0, giving the root x = 5.

If the quadratic equation x^2 - 10x + 25 = 0 is solved, what is the value of x? (2022)

If the quadratic equation x^2 - 10x + 25 = 0 is solved, what is the value of x? (2022)

Step 1: Start with the quadratic 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 be simplified to (x - 5)^2 = 0.
Step 6: To find the value of x, set (x - 5) equal to 0: x - 5 = 0.
Step 7: Solve for x by adding 5 to both sides: x = 5.

Quadratic Equations – Understanding how to solve quadratic equations through factoring, completing the square, or using the quadratic formula.
Factoring – Recognizing perfect square trinomials and factoring them correctly.