Completing The Square

Question 1

A student says that if 5x2 = 20, then x must be equal to 2. Do you agree or disagree with the student? Justify your answer.

Revolt · Accepted Answer

Disagree. Dividing both sides by 5 gives x² = 4. By the square root property, x = 2 or x = -2. Therefore, x could also be -2.

Question 2

The solution to 3x2 – 12x + 24 = 0 is 7 or –7✔ 2 + 2i or 2 – 2i12 or –2.

Revolt · Accepted Answer

✔ 2 + 2i or 2 – 2i

Question 3

First, subtract from each side of the equation.

Revolt · Accepted Answer

60

Question 4

Next, add to each side of the equation to complete the square.

Revolt · Accepted Answer

64

Question 5

Now, write x² - 16x + 64 = -8 as (x - 8)² = -16✔ (x - 8)² = -8(x - 16)² = -16(x - 16)² = -8

Revolt · Accepted Answer

✔ (x - 8)² = -8

Question 6

Solve x2 - 16x + 60 = -12 by completing the steps.

Revolt · Accepted Answer

8; 2

Question 7

Consider 8x2 - 48x = -104. Write the equation so that Complete the square:

Revolt · Accepted Answer

a = 1: x2 +: -6; =: -13

Question 8

Consider 8x2 - 48x = -104. Write the equation so that Complete the square:

Revolt · Accepted Answer

x2 – 6x +: 9; –13 +: 9

Question 9

Consider 8x2 - 48x = -104. Write the equation so that Complete the square:

Revolt · Accepted Answer

(x +: -3; =: -4

Question 10

Use the square root property of equality to solve(x – 3)2 = –4.The solutions are –1 or 71 or 5✔ 3 ± 2i3 ± 4i.

Revolt · Accepted Answer

✔ 3 ± 2i

Completing The Square Answers