Completing the Square

​Solving Quadratic Equations by Completing The Square

​Completing the square

​Example 1. Complete the square of x² + 14x _____. Then write it in factored form.

​Example 2. Complete the square of x² - 5x _____. Then write it in factored form.

Multiple Choice

Complete the square.

$$x^2\ -3x$$  

• $$x^2-3x\ +\ \frac{9}{4}$$  

• $$x^2-3x-\frac{9}{4}$$  

• $$x^2-3x+9$$  

• $$x^2-3x^2-9$$  

Multiple Choice

What expression must be added to x² + 10x to complete the square?

• 5

• 25

• 100

Multiple Choice

What is the factored form of x² + 18x + 81?

• (x + 9)²

• (x - 9)²

• (x + 6)²

• (x - 6)²

​Example 3. Solve x² + 8x + 2 = 0 by completing the square.

​Example 4. Solve x² - 5x + 6 = 0 by completing the square.

​Example 4. Solve x² - 5x + 6 = 0 by completing the square.

Draw

Solve by completing the square.

x² - 2x - 12 = 0

Multiple Choice

Find the value that completes the square
$$x^2-8x+c$$

• $$16$$  
  

• $$4$$  

• $$8$$

• $$64$$  
  

Multiple Choice

Find the value that completes the square
$$x^2+28x+c$$   

• $$81$$  
  

• $$784$$  

• $$196$$

• $$14$$  
  

Multiple Choice

$$f\left(x\right)=x^2+2x-15$$  

Complete the square and find the zeros

• $$x=-3,-5$$  

• $$x=3,-5$$  

• $$x=3,5$$  

• $$x=-3,5$$  

Multiple Choice

$$f\left(x\right)=x^2-16x+43$$  

Complete the square and find the zeros

• $$x=-16\pm\sqrt{21}$$  

• $$x=16\pm\sqrt{21}$$  

• $$x=-8\pm\sqrt{21}$$  

• $$x=8\pm\sqrt{21}$$  

Multiple Choice

$$f\left(x\right)=2x^2-20x+10$$  

Complete the square and find the zeros

• $$x=5\pm\sqrt{20}$$  

• $$x=-5\pm\sqrt{20}$$  

• $$x=-10\pm\sqrt{20}$$  

• $$x=10\pm\sqrt{20}$$  

Multiple Choice

$$4x^2+16x+1=-6$$  

Complete the square and find the zeros

• $$x=2\pm\sqrt{\frac{9}{4}}$$  

• $$x=-2\pm\sqrt{\frac{9}{4}}$$  

• $$x=-2\pm\sqrt{9}$$  

• $$x=2\pm\sqrt{9}$$  

Multiple Choice

What is the Perfect Square Trinomial given the binomial square $$\left(x+8\right)^2$$  ?

• $$x^2+16x\ +64$$   

• $$x^2-16x\ +64$$  

• $$x^2+16x\ -64$$  

• $$x^2+16x\ +16$$