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coldgirl [10]
3 years ago
7

Use the quadratic formula to solve x^2+8x+9=0

Mathematics
1 answer:
Tju [1.3M]3 years ago
4 0
None of your options, not via complete the square nor quadratic the formula.

Solve for x over the real numbers:
x^2 + 8 x + 9 = 0

x = (-8 ± sqrt(8^2 - 4×9))/2 = (-8 ± sqrt(64 - 36))/2 = (-8 ± sqrt(28))/2:
x = (-8 + sqrt(28))/2 or x = (-8 - sqrt(28))/2

sqrt(28) = sqrt(4×7) = sqrt(2^2×7) = 2sqrt(7):
x = (2 sqrt(7) - 8)/2 or x = (-2 sqrt(7) - 8)/2

Factor 2 from -8 + 2 sqrt(7) giving 2 (sqrt(7) - 4):
x = 1/22 (sqrt(7) - 4) or x = (-2 sqrt(7) - 8)/2

(2 (sqrt(7) - 4))/2 = sqrt(7) - 4:
x = sqrt(7) - 4 or x = (-2 sqrt(7) - 8)/2

Factor 2 from -8 - 2 sqrt(7) giving 2 (-sqrt(7) - 4):
x = sqrt(7) - 4 or x = 1/22 (-sqrt(7) - 4)

(2 (-sqrt(7) - 4))/2 = -sqrt(7) - 4:

Answer: x = sqrt(7) - 4 or x = -sqrt(7) - 4_____________________________________________________

Solve for x:
x^2 + 8 x + 9 = 0

Subtract 9 from both sides:
x^2 + 8 x = -9

Add 16 to both sides:
x^2 + 8 x + 16 = 7

Write the left hand side as a square:
(x + 4)^2 = 7

Take the square root of both sides:
x + 4 = sqrt(7) or x + 4 = -sqrt(7)

Subtract 4 from both sides:
x = sqrt(7) - 4 or x + 4 = -sqrt(7)

Subtract 4 from both sides:
Answer:  x = sqrt(7) - 4 or x = -4 - sqrt(7)
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Ede4ka [16]

Answer:

Please check the attached diagram.

Thus, we conclude that:

In the diagram,

  • The red line represents the parent function f(x) = x
  • The blue line represents the function f(x) = x+1

The blue line indicates that the parent function has been shifted 1 unit upward.

Step-by-step explanation:

Let us recall some transformation knowledge.

We know that

if y = f(x), then y = f(x) + b simply means a transformation of (0, b).

In other words, if we add some constant let say 'b' in the output or y-value, the graph simply shifts upward by b units.

Given that

f(x) = x

so

f(x+1) = x+1 means the parent function f(x) = x has been shifted 1 unit upward.

Please check the attached diagram.

Thus, we conclude that:

In the diagram,

  • The red line represents the parent function f(x) = x
  • The blue line represents the function f(x) = x+1

The blue line indicates that the parent function has been shifted 1 unit upward.

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Tomato paste is sold in a cylindrical can. The can has a radius of 2 inches and a height of 6 inches. What is the volume of the
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<h3>Answer:  24pi  cubic inches</h3>

Work Shown:

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