If x² - 25 = 0, then x = ?
Understand the Problem
The question is asking to solve the equation x² - 25 = 0 for the variable x. This involves algebraic manipulation to find the value of x.
Answer
The solutions are \(x = 5\) and \(x = -5\).
Answer for screen readers
The solutions to the equation (x^2 - 25 = 0) are (x = 5) and (x = -5).
Steps to Solve
- Set the equation to zero
We start with the equation given: $$x^2 - 25 = 0$$
- Add 25 to both sides
To isolate the (x^2) term, we add 25 to both sides of the equation: $$x^2 = 25$$
- Take the square root of both sides
Next, we take the square root of both sides to solve for (x): $$x = \pm \sqrt{25}$$
- Simplify the square root
The square root of 25 is 5, so: $$x = \pm 5$$
This gives us the two possible solutions.
The solutions to the equation (x^2 - 25 = 0) are (x = 5) and (x = -5).
More Information
This equation is a difference of squares, which is a common type of quadratic equation. It can be factored into ((x - 5)(x + 5) = 0).
Tips
A common mistake is to forget the plus-minus sign when taking the square root. Remember that taking the square root of a number gives both a positive and a negative solution.
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