Solve an equation by using the square root method

The video tutorial covers solving equations, focusing on factoring and the quadratic formula. It explains nonfactorable equations and introduces perfect square trinomials. The instructor demonstrates factoring these trinomials and solving equations using the square root method, emphasizing the importance of including both positive and negative roots.

What is the first step when you cannot solve an equation directly?

• Multiply both sides by a variable

• Add a constant to both sides

• Set the equation equal to zero

• Divide both sides by a constant

When an equation is non-factorable, which method can be used as an alternative?

• Quadratic formula

• Exponential method

• Cubic formula

• Linear method

What is a key characteristic of a perfect square trinomial?

• The middle term is half the square of the last term

• The first term is a prime number

• The last term is a cube number

• The last term is a square number

How can a perfect square trinomial be factored?

• As a product of two different binomials

• As a sum of cubes

• As a single term

• As a squared binomial

What must be considered when taking the square root of both sides of an equation?

• Only the negative root

• Only the positive root

• Neither root

• Both positive and negative roots

What are the solutions for the equation x + 6 squared equals 25?

• x = 6 and x = -6

• x = 5 and x = -5

• x = -1 and x = -11

• x = 1 and x = 11

Why is it necessary to include both positive and negative signs when introducing a square root?

• Because the square root is always negative

• Because it simplifies the equation

• Because both positive and negative numbers can square to the same value

• Because the square root is always positive