What is the first step in completing the square for the equation $$x^2 + 6x - 4 = 36$$ ?

Subtract 36 from both sides to set the equation to zero: $$x^2 + 6x - 40 = 0$$ .

What is the new C-term for the equation $$x^2 + 6x - 4 = 36$$ ?

For the equation, b = 6, so the new C-term is $$C = \left(\frac{6}{2}\right)^2 = 9$$ .

What is the completed square form of the equation $$x^2 + 6x - 40 = 0$$ ?

The completed square form is $$(x + 3)^2 - 49 = 0$$ .

How do you solve the equation $$(x + 3)^2 - 49 = 0$$ ?

Add 49 to both sides: $$(x + 3)^2 = 49$$ , then take the square root: $$x + 3 = \pm 7$$ .

What are the roots of the equation $$x^2 + 6x - 4 = 36$$ after completing the square?

The roots are $$x = 4$$ and $$x = -10$$ .

What is the first step to solving the equation $$a^2 + 10a + 21 = 0$$ by completing the square?

Subtract 21 from both sides to set the equation to zero: $$a^2 + 10a = -21$$ .

What is the completed square form of the equation $$n^2 - 2n - 3 = 0$$ ?

The completed square form is $$(n - 1)^2 - 4 = 0$$ .

What are the roots of the equation $$n^2 - 2n - 3 = 0$$ after completing the square?

The roots are $$n = 3$$ and $$n = -1$$ .

Solve the equation $$x^2 - 14x - 15 = 0$$ by completing the square.

The roots are $$x = -1$$ and $$x = 15$$ .

What is the significance of the term 'perfect square trinomial'?

A perfect square trinomial is an expression that can be factored into the square of a binomial, typically in the form $$(a + b)^2 = a^2 + 2ab + b^2$$ .

What does it mean to 'set the equation to zero' in the context of completing the square?

Setting the equation to zero means rearranging the equation so that one side equals zero, which is necessary for applying the completing the square method.

Why is completing the square useful in solving quadratic equations?

Completing the square allows us to rewrite a quadratic equation in a form that makes it easier to find the roots, especially when the quadratic does not factor neatly.

Completing the square Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial, which makes it easier to find the roots.

Tags

CCSS.HSA-REI.B.4B

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

How do you find the new C-term when completing the square?

Back

Tags

CCSS.HSA-REI.B.4B

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

6.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

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