Question
Solve for \( x \) in the following equation \( x^{2}-25=0 \)
Ask by Chan Mann. in South Africa
Nov 11,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x=-5 \) or \( x=5 \).
Solution
Solve the equation \( x^{2}-25=0 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(x^{2}-25=0\)
- step1: Add or subtract both sides:
\(x^{2}=25\)
- step2: Simplify the expression:
\(x=\pm \sqrt{25}\)
- step3: Simplify the expression:
\(x=\pm 5\)
- step4: Separate into possible cases:
\(\begin{align}&x=5\\&x=-5\end{align}\)
- step5: Rewrite:
\(x_{1}=-5,x_{2}=5\)
The solutions for the equation \( x^{2}-25=0 \) are \( x=-5 \) and \( x=5 \).
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Simplify this solution The Deep Dive
To solve the equation \( x^{2}-25=0 \), we can start by adding 25 to both sides: \[ x^{2} = 25 \] Next, we take the square root of both sides. Remember, when you take the square root, you can have both a positive and a negative solution: \[ x = \pm 5 \] So, the solutions are \( x = 5 \) and \( x = -5 \). Now you've discovered two possible values for \( x \)!
