Mastering Completing the Square in Quadratics

Mr. Champlin explains how to solve quadratic equations using the method of completing the square. He demonstrates the process with two examples, highlighting the importance of this method even when factoring is possible. The video covers solving quadratics with rational roots and converting solutions to the simplest radical form. The tutorial emphasizes understanding each step, including dividing the B value, creating a perfect trinomial, and solving for x. The video concludes with tips on using a calculator for decimal approximations and simplifying radical expressions.

What is the first step in solving a quadratic equation by completing the square?

• Square the B value

• Divide the B value by 2

• Add the squared B value to both sides

• Set the equation to zero

What do you do after finding the number to complete the square?

• Add it to the equation

• Multiply it by 2

• Subtract it from both sides

• Add and subtract it inside the equation

How do you solve the equation after forming a perfect square trinomial?

• Factor the trinomial

• Take the square root of both sides

• Divide by the leading coefficient

• Graph the equation

What is the result of taking the square root of both sides of the equation?

• A perfect square

• An undefined expression

• Two values of x

• A single value of x

What indicates that a quadratic equation might have rational roots?

• It can be easily factored

• It cannot be factored

• Its leading coefficient is 1

• Its B value is even

How do you find the value to add and subtract when completing the square?

• Square the B value

• Multiply the B value by the leading coefficient

• Divide the C value by 2

• Divide the B value by 2 and square it

What is the purpose of adding and subtracting the same value inside the equation?

• To form a perfect square trinomial

• To eliminate the B value

• To balance the equation

• To simplify the equation

How do you handle irrational roots when solving quadratic equations?

• Round them to the nearest tenth

• Leave them in square root form

• Convert them to decimals

• Ignore them

What is the correct way to simplify the square root of 18 to its simplest radical form?

• √9 * √2

• 9√2

• 3√2

• 6√3

What does it mean to express a solution in its simplest radical form?

• The solution is rounded to the nearest whole number

• The solution is expressed as a decimal

• The solution is left as an unsimplified square root

• The solution is simplified using radical notation