1. Complete the square to form a perfect square trinomial. 8x + x² + __

1 answer:

7 0

1. x² + 8x + 16
x² + 4x + 4x + 16
x(x) + x(4) + 4(x) + 4(4)
x(x + 4) + 4(x + 4)
(x + 4)(x + 4)
(x + 4)²
The answer is A.

2.   x² + 4x = 12
  x² + 4x + 4 = 12 + 4
  x² + 4x + 4 = 16
  x² + 2x + 2x + 4 = 16
x(x) + x(2) + 2(x) + 2(2) = 16
x(x + 2) + 2(x + 2) = 16
(x + 2)(x + 2) = 16
  (x + 2)² = 16
  √(x + 2)² = √16
x + 2 = ±4
  - 2 - 2
x = -2 ± 4
x = -2 + 4 or x = -2 - 4
x = 2   or x = -6
The answer is B.

3. x² + 9x + 4 = 0
  Δ = b² - 4ac
  Δ = (9)² - 4(1)(4)
  Δ = 81 - 4(4)
  Δ = 81 - 16
  Δ = 65
THe answer is C.

4. x² - 6x - 7 = 0
  Δ = b² - 4ac
  Δ = (-6)² - 4(1)(-7)
  Δ = 36 - 4(-7)
  Δ = 36 + 28
  Δ = 64
The answer is A.

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Add: 3x+9+8x + 12 2x + 6+x² + 6x + 9

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I'll treat these like they're two seperate problems because how you set it up they're not together. If it's one whole problem please tell me and I'll solve it that way. :-)

First one: 3x+9+8x + 12

Collect like terms and simplify

(3x+8x)+(9+12)

11x+21

Second one: 2x + 6+x² + 6x + 9

Collect like terms and simplify

$(2x+6x)+(6+9)+x^{2}$