How do you complete the square to solve #x^2 + 6x + 34 = 0#?

Answer 1
#x^2+6x+34 = 0# can be written as #color(white)("XXXX")##x^2+6x = -34#
completing the square: #color(white)("XXXX")##x^2+6x+9 = -25# #color(white)("XXXX")##(x+3)^2 = -25# take the square root of both sides #color(white)("XXXX")##x+3 = sqrt(-25)##color(white)("XXXX")#(Note: no Real solutions)
#color(white)("XXXX")##x= -3 +-5i#
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Answer 2

To solve the equation x^2 + 6x + 34 = 0 by completing the square:

  1. Move the constant term to the other side of the equation: x^2 + 6x = -34.
  2. To complete the square, take half of the coefficient of x (6/2 = 3), square it (3^2 = 9), and add it to both sides of the equation: x^2 + 6x + 9 = -34 + 9.
  3. Simplify: (x + 3)^2 = -25.
  4. Take the square root of both sides: x + 3 = ±√(-25).
  5. Simplify: x + 3 = ±5i.
  6. Subtract 3 from both sides: x = -3 ± 5i.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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