Solve each equation in Exercises 60–63 by the square root property. x^2/2 + 5 = -3

Key Concepts

Square Root Property

The square root property states that if x^2 = k, then x = ±√k. This property is essential for solving quadratic equations, as it allows us to isolate the variable by taking the square root of both sides. It is particularly useful when the equation is in the form of x^2 = a constant, enabling straightforward solutions.

Isolating the Variable

Isolating the variable involves rearranging an equation to get the variable on one side and all other terms on the opposite side. This step is crucial in solving equations, as it simplifies the problem and allows for the application of methods like the square root property. In the given equation, isolating x^2 is the first step before applying the square root property.

Quadratic Equations

Quadratic equations are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants. They can have zero, one, or two real solutions, depending on the discriminant (b^2 - 4ac). Understanding the nature of quadratic equations is vital for applying various solving techniques, including factoring, completing the square, and using the square root property.