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vfiekz [6]
2 years ago
5

16) w(x) = 4x + 4; Find w(x + 4)

Mathematics
1 answer:
Zina [86]2 years ago
3 0

\\ \tt\hookrightarrow w(x)=4x+4=4(x+1)

Now

\\ \tt\hookrightarrow w(x+4)=4(x+4+1)

\\ \tt\hookrightarrow w(x+4)=4(x+5)

\\ \tt\hookrightarrow w(x+4)=4x+20

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4. (x + 3)² = 27

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Taking the constant term to the other side, we get:

x² - 6x = - 1

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⇒ x² -2(3)x + 9 = - 1 + 9  [Adding 9 to both the sides]

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Note that the co-effecient of x² is not 1. We make it 1, by dividing the whole equation by 3. And then proceed like the previous problem.

3x² + 12x = -3

Dividing by 3 through out, x² + 4x = - 1

⇒ x² + 2(2) + 4 = -1 + 4

⇒ x² +2(2) + 2² = 3

⇒ (x + 2)² = 3 is the answer.

3. 2x² + 24x = 29

x² + 12x = $ \frac{29}{2} $

⇒ x² + 2(6)x + 36 = $ \frac{29}{2} $ + 36

⇒ x² + 2(6)x + 6² = $ \frac{29 + 72}{2} $

⇒ (x + 6)² = $ \frac{101}{2} $ is the answer.

4. x² + 6x - 18 = 0

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⇒ x² + 2(3)x = 18

⇒ x² + 2(3)x + 9 = 18 + 9

⇒ x² + 2(3)x + 3² = 27

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5. x² + 8x + 3 = 0

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⇒ x² + 2(4)x + 16 = - 3 + 16

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$ \bigg( x - \frac{15}{9} \bigg) ^2 = \frac{261}{81} = \frac{29}{9} $ is the answer.

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