Completing the Square - Day 2

Completing the Square
(When a > 1)

By Melinda Austin

Drag and Drop

The first step would be ​

Placeholder

Drag these tiles and drop them in the correct blank above

add 5 to both sides

divide 8 by 2

raise 4 to the 2nd power

Drag and Drop

What would the next step be? ​

Placeholder

Drag these tiles and drop them in the correct blank above

divide 8 by 2

raise 4 to the 2nd power

divide each term by 4

add 5 to both sides

Drag and Drop

What should the third step look like? ​​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Drag and Drop

What should the fourth step look like? ​​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Drag and Drop

What should the fifth step look like? ​​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Multiple Choice

Given the equation: $$2x^2-8x+6=0$$ What is the first step in solving the equation by Completing the Square?

• $$2x^2-8x=-6$$

• $$x^2-4x=-3$$

• $$-\frac{4}{2}=\left(-2\right)^2$$

• $$x^2-4x+4=-3+4$$

Multiple Choice

Given the equation: $$2x^2-8x+6=0$$ What is the second step in solving the equation by Completing the Square?

• $$2x^2-8x=-6$$

• $$x^2-4x=-3$$

• $$-\frac{4}{2}=\left(-2\right)^2$$

• $$x^2-4x+4=-3+4$$

Multiple Choice

Given the equation: $$2x^2-8x+6=0$$ What is the third step in solving the equation by Completing the Square?

• $$2x^2-8x=-6$$

• $$x^2-4x=-3$$

• $$-\frac{4}{2}=\left(-2\right)^2$$

• $$x^2-4x+4=-3+4$$

Multiple Choice

Given the equation: $$2x^2-8x+6=0$$ What is the fourth step in solving the equation by Completing the Square?

• $$\sqrt[]{2x^2-8x}=\sqrt[]{-6}$$

• $$\sqrt[]{\left(x-2\right)^2}=\sqrt[]{1}$$

• $$\sqrt[]{-\frac{4}{2}}=\sqrt[]{\left(-2\right)^2}$$

• $$\sqrt[]{\left(x+2\right)^2}=\sqrt[]{1}$$

Match

$$3x^2-18x-48=0$$

Match the correct equation to the correct step in solving the given equation by Completing the Square?

• 1st step

• 2nd step

• 3rd step

• 4th step

• 5th step

• $$3x^2-18x=48$$

• $$x^2-6x=16$$

• $$x^2-6x+9=16+9$$

• $$\left(x-3\right)^2=25$$

• $$\sqrt[]{\left(x-3\right)^2}=\sqrt[]{25}$$

Match

$$5x^2+10x-34=6$$

Match the correct equation to the correct step in solving the given equation by Completing the Square?

• 1st step

• 2nd step

• 3rd step

• 4th step

• 5th step

• $$5x^2+10x=40$$

• $$x^2+2x=8$$

• $$x^2+2x+1=8+1$$

• $$\left(x+1\right)^2=9$$

• $$\sqrt[]{\left(x+1\right)^2}=\sqrt[]{9}$$

Complete problems 4, 5, and 6.

​Work with your table.

Let's look at numbers 7 and 8.

​Regroup! Irrational Solutions

Multiple Select

9. The solution to the equation $$3x^2-6x-3=90$$ . Select all that apply.

• $$x=3+\sqrt[]{13}$$

• $$x=3-\sqrt[]{13}$$

• $$x=-3+\sqrt[]{13}$$

• $$x=-3-\sqrt[]{13}$$

Multiple Select

10. The solution to the equation $$5x^2+30x-4=16$$ . Select all that apply.

• $$x=1+4\ \sqrt[]{2}$$

• $$x=1+16\ \sqrt[]{2}$$

• $$x=1-4\ \sqrt[]{2}$$

• $$x=1-16\ \sqrt[]{2}$$