What are the solution(s) to the quadratic equationx2–25=0x^2 – 25 = 0x2–25=0?

Step 1: Define the Problem

Identify the key components of the question that need to be addressed:

• Solve the quadratic equation $x^2 - 25 = 0$.

Step 2: Break Down the Problem

Divide the problem into smaller, manageable parts:

• Recognize that this is a difference of squares.

Step 3: Apply Relevant Concepts

Use appropriate academic theories or formulas to solve each part of the problem:

• The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$.

Step 4: Analysis, Verify and Summarize

Analysis each part in detail if necessary, carry out the calculations by steps:

• Rewrite the equation using the difference of squares: $x^2 - 25 = (x - 5)(x + 5) = 0$
• Set each factor equal to zero and solve for $x$: $x - 5 = 0 \quad \Rightarrow \quad x = 5$ $x + 5 = 0 \quad \Rightarrow \quad x = -5$

Final Answer

Present the final result in a concise manner:

• The solutions to the quadratic equation $x^2 - 25 = 0$ are $x = 5$ and $x = -5$.