Lesson 3.4: Completing The Square Answers
Which of the following expressions are perfect-square trinomials? Check all of the boxes that apply.
x² - 5x + 5/25/4✔ 25/4
x² + ✔ 1477/2 x + 49
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.
I disagree with the student. While 2 is a solution, it is not the only possible value for x. Dividing both sides of the equation 5x^2 = 20 by 5 results in x^2 = 4. According to the square root property, taking the square root of both sides gives x = 2 or x = -2. Therefore, x could be -2 as well.
Compare your response with the sample response presented here. Did your explanation
Given (x – 7)2 = 36, select the values of x.
Given (x – 1)2 = 50, select the values of x.
Now, write x² - 16x + 64 = -8 as (x - 8)² = -16✔ (x - 8)² = -8(x - 16)² = -16(x - 16)² = -8
.
2
⇒ 8
8
Consider 8x2 - 48x = -104. Write the equation so that Complete the square:
=
-13
Consider 8x2 - 48x = -104. Write the equation so that Complete the square:
–13 +
9
Consider 8x2 - 48x = -104. Write the equation so that Complete the square:
=
-4
Use the square root property of equality to solve(x – 3)2 = –4.The solutions are –1 or 71 or 5✔ 3 ± 2i3 ± 4i.
The solution to x2 – 10x = 24 is 7 or –72 + 2i or 2 – 2i✔ 12 or –2.
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