Solve each equation in Exercises 15–34 by the square root property. 5x^2 = 45

Verified step by step guidance

1. First, isolate the term with the variable by dividing both sides of the equation by 5: \( x^2 = \frac{45}{5} \).
2. Simplify the right side of the equation: \( x^2 = 9 \).
3. Apply the square root property, which states that if \( x^2 = a \), then \( x = \pm \sqrt{a} \).
4. Take the square root of both sides: \( x = \pm \sqrt{9} \).
5. Simplify the square root: \( x = \pm 3 \).

Key Concepts

Square Root Property

The square root property states that if an equation is in the form of x^2 = k, where k is a non-negative number, then the solutions for x can be found by taking the square root of both sides. This results in x = ±√k. This property is essential for solving quadratic equations that can be expressed in this standard form.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. They can be solved using various methods, including factoring, completing the square, and applying the square root property. Understanding the structure of quadratic equations is crucial for identifying the appropriate method for solving them.

Isolating the Variable

Isolating the variable involves rearranging an equation to get the variable on one side and the constants on the other. In the context of the square root property, this means manipulating the equation to express it in the form x^2 = k before applying the square root. This step is vital for correctly applying the square root property to find the solutions.