Completing The Square Answers
Which of the following expressions are perfect-square trinomials? Check all of the boxes that apply.
x² + x + 49
Now, write x² - 16x + 64 = -8 as (x - 8)² = -16✔ (x - 8)² = -8(x - 16)² = -16(x - 16)² = -8
Solve x2 - 16x + 60 = -12 by completing the steps.
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Use the square root property of equality to solve(x – 3)2 = –4.The solutions are –1 or 71 or 5✔ 3 ± 2i3 ± 4i.
x² - 5x +
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.
Given (x – 7)2 = 36, select the values of x.
What method would you choose to solve the equation 2x2 – 7 = 9? Explain why you chose this method.
I would use the square root property to solve the equation. Since there is no linear xterm, I can isolate the x^2 term by adding 7 to both sides and then dividing by 2. This leaves x^2 8, which can then be solved by taking the square root of both sides.
a = 1: x2 + x
-6
x2 – 6x + =
9
(x + )²
-3
The solution to x2 – 10x = 24 is 7 or –72 + 2i or 2 – 2i✔ 12 or –2.
Complete the square to write 16t² - 96t + 48 = 0 as (t + 9)² = -3✔ (t - 3)² = 6(t - 6)² = 12.
Compare your response with the sample response presented here. Did your explanation
Given (x – 1)2 = 50, select the values of x.
Which points did you include in your response? Check all of the boxes that apply.
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