Solve the equation by completing the square.
- + 4x - 21 = 0
B) -3, 7
C) -7, 3
D) -7, -14

Question

Solve the equation by completing the square.
- + 4x - 21 = 0
B) -3, 7 
C) -7, 3 
D) -7, -14

Quizplus · Accepted Answer

To complete the square, first move the constant term to the other side of the equation:

11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11 + 4x = 21

Next, factor out the coefficient of x, which is 4:

11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11 + 4(x + 11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11/4) = 21 + 11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11/4

Now we can see that the expression inside the parentheses is the completed square form of x. To simplify, we can write:

11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11 + 4(x + 11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11/4) = 11ebb63d_1bdc_fd79_b851_8daf9c1ee8f7_TB8475_11/4 + 21

Finally, solve for x:

x + 11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11/4 = (11ebb63d_1bdc_fd79_b851_8daf9c1ee8f7_TB8475_11/4 + 21) / 11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11

x = (11ebb63d_1bdc_fd79_b851_8daf9c1ee8f7_TB8475_11/4 + 21) / 11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11 - 11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11/4

x = (-7, 3) Start by isolating the x term:

11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11 + 4x - 21 = 0
11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11 + 4x = 21
4x = -11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11 + 21

Now complete the square on the x term:

4x = -11ebb63d_1bdc_fd79_b851_8dc687501bfb_TB8475_11 + 21
4x = -11ebb63d_1bdc_fd7a_b851_07ab9958ae60_TB8475_11
x = (-11ebb63d_1bdc_fd7a_b851_07ab9958ae60_TB8475_11) / 4

Simplify to get:

x = -7 or x = 3

So the answer is C.

Solve the Equation by Completing the Square