Question

????????????????? :)​

Answer 1

(x-3)²-14

Explanation:

Complete the square of the following quadratic equation.

x²-6x-5

`\hrulefill`

To complete the square for a quadratic equation in the form of ax²+bx+c =0, where a, b, and c are constants, you can follow these steps:

1. Make sure the coefficient of x^2 is 1. If it's not, divide the entire equation by that coefficient.
2. Move the constant term (c) to the other side of the equation.
3. Split the coefficient of x (b) into two equal halves, and square the result.
4. Add the squared value obtained in step 3 to both sides of the equation.
5. Write the left side of the equation as a perfect square trinomial.
6. Simplify the right side of the equation, if necessary.
7. Now, the equation is in the form of (x+a)²=b, where a and b are constants.

`\hrulefill`

Step (1):

x²-6x-5=0

=> (1)x²-6x-5=0

a=1, so we can proceed

Step (2):

x²-6x=5

Step (3):

b=-6

=>1/2b=-3

=> (-3)²=9

Step (4):

x²-6x+9=5+9

Step (5):

(x-3)²=5+9

Step (6 & 7):

(x-3)²=14

We can rewrite this to get it in the form for your question.

(x-3)²=14

=> (x-3)²-14

Thus, the blanks are 3 and 14.