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(a) Complete the square by writing in the form . Note: the numbers and can be positive or negative.


x^2-14x-17=(x-7)^2+

(b) Solve the equation by completing the square or using the quadratic formula. If there is more than one correct answer, enter your answers as a comma separated list. If there are no solutions, enter NONE.

x^2-14x-17=0

I keep getting this wrong but I don't know why.help please

User Icon for Reiny Reiny answered
12 years ago

x^2 - 14x + .... = 17 + ....

x^2 - 14x + 49 = 17+ 49
(x-7)^2 = 66
x-7 = ± √66
x = 7 ± √66

by formula:
x = (14 ± √(14^2 - 4(1)(-17))/2
= (14 ± √264)/2
= (14 ± 2√66)/2
= 7 ± √66

When the coefficient of x^2 is 1 and the middle term is even, I always use "completing the square" rather than the formula. Notice you get the answer already in simplified form

User Icon for Explain Bot Explain Bot answered
11 months ago

To complete the square and solve the equation x^2 - 14x - 17 = 0, follow these steps:

(a) Completing the Square:
Step 1: Move the constant term (-17) to the right side of the equation by adding 17 to both sides:
x^2 - 14x = 17

Step 2: Take half of the coefficient of x (-14 in this case) and square it. So, (-14/2)^2 = 49.
Add 49 to both sides of the equation:
x^2 - 14x + 49 = 17 + 49

Step 3: Simplify and rewrite the equation:
(x - 7)^2 = 66

Hence, by completing the square, the equation becomes (x - 7)^2 = 66.

(b) Solving the Equation:
Step 4: Take the square root of both sides of the equation:
√[(x - 7)^2] = ±√66

Step 5: Solve for x by considering both the positive and negative square roots:
(x - 7) = ±√66

For the positive square root:
x - 7 = √66
x = 7 + √66
x = 7 + √(2 * 33)
x = 7 + √(2 * 3^2 * 11)
x = 7 + 3√22

For the negative square root:
x - 7 = -√66
x = 7 - √66
x = 7 - √(2 * 3^2 * 11)
x = 7 - 3√22

Therefore, the solutions to the equation x^2 - 14x - 17 = 0 are:
x = 7 + 3√22, 7 - 3√22.