Learn to describe and solve for the zeros using completing the square

The video tutorial explores solving a quadratic equation by factoring, quadratic form, and completing the square. Initial attempts at factoring are unsuccessful, leading to the use of completing the square. The process involves isolating variables, factoring out constants, and using the formula B/2 squared. The solution is simplified to find the roots, which are identified as irrational due to the presence of sqrt 2. The tutorial concludes by comparing the solution to what would be obtained using the quadratic formula.

What was the main issue encountered when trying to factor the quadratic equation using 4X * X and 2X * 2X?

• The equation had no real solutions.

• The equation was already factored.

• The coefficients were too large.

• The middle terms did not match.

What is the first step in the completing the square method?

• Factor the equation completely.

• Add a constant to both sides.

• Isolate the variable terms on one side.

• Multiply both sides by a constant.

Why is it necessary to factor out a constant before completing the square?

• To simplify the equation.

• To eliminate the linear term.

• To ensure the quadratic term has a coefficient of 1.

• To make the equation homogeneous.

After completing the square, what operation is used to solve for X?

• Multiplication

• Addition

• Square root

• Division

What type of solutions are obtained for the quadratic equation in this example?

• Imaginary

• Real and irrational

• Complex

• Real and rational