Solve each equation in Exercises 15–34 by the square root property. 2x^2 - 5 = - 55

Verified step by step guidance

1. First, isolate the quadratic term by adding 55 to both sides of the equation: \(2x^2 - 5 + 55 = 0 + 55\).
2. Simplify the equation: \(2x^2 + 50 = 0\).
3. Next, divide every term by 2 to simplify further: \(x^2 + 25 = 0\).
4. Now, isolate \(x^2\) by subtracting 25 from both sides: \(x^2 = -25\).
5. Apply the square root property: \(x = \pm \sqrt{-25}\).

Key Concepts

Square Root Property

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

Rearranging Equations

Rearranging equations involves manipulating the equation to isolate the variable of interest. In the context of the given problem, this means moving all terms to one side to set the equation equal to zero or to isolate the squared term. This step is crucial for applying the square root property effectively.

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 vital for identifying the appropriate method for solving them.