Match the equation in Column I with its solution(s) in Column II. x² = 25

Verified step by step guidance

1. Identify the type of equation given: \(x^2 = 25\) is a quadratic equation in the form \(x^2 = c\), where \(c\) is a positive constant.
2. Recall the property that if \(x^2 = c\), then \(x = \pm \sqrt{c}\). This means the solutions are both the positive and negative square roots of \(c\).
3. Apply this property to the equation: \(x = \pm \sqrt{25}\).
4. Simplify the square root: \(\sqrt{25} = 5\), so the solutions are \(x = 5\) and \(x = -5\).
5. Match these solutions to the options in Column II that list \(x = 5\) and \(x = -5\) as the solutions.

Key Concepts

Solving Quadratic Equations

A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. Solving such equations involves finding values of x that satisfy the equation, often by factoring, using the quadratic formula, or isolating the variable when possible.

Square Roots and Their Properties

Taking the square root of both sides of an equation like x² = 25 involves understanding that both positive and negative roots are possible. Specifically, if x² = a, then x = ±√a, meaning the solutions include both the positive and negative square roots.

Matching Equations to Solutions

Matching equations to their solutions requires recognizing the form of the equation and applying appropriate solution methods. For x² = 25, identifying that the solutions are x = 5 and x = -5 helps correctly pair the equation with its solution set.