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nekit [7.7K]
3 years ago
12

Complete the square y=x^2+6x+8

Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
8 0

Answer:

y = (x+3)² - 1

Step-by-step explanation:

To complete the square take the middle term b and divide by 2. Then square the value.

Here b = 6.

So 6/2 = 3

3² = 9

Add 9 to both sides of the equation.

x² + 6x + 8 = 0

x² + 6x + 9 + 8 = 9

(x+3)² - 1 = y

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To Rationalize the denominator of 5-√7/9-√14, you should multiply the expression by which fractions?
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<u>Answer</u>

9+√14


<u>Explanation</u>

To Rationalize the denominator of 5-√7/9-√14.

To rationalize this we multiply both the denominator and denominator by the conjugate of the denominator.

The denominator is 9-√14 and its conjugate is (9+√14).

(5-√7)/(9-√14) = (5-√7)(9+√14)/(9-√14)(9+√14)

                        =  (5-√7)(9+√14)/(9²-14)

                       = (45 + 5√14 - 9√7 - √98)/(81-14)

                        =  (45 + 5√14 - 9√7 - √98)/67

                        = (45 + 5√14 - 9√7 - 7√2)67

This is the rationalized expression.  

The denominator is (9-√14) and its conjugate is (9+√14).

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