How do you solve the quadratic equation by completing the square: #x^2 + 4x = 21#?

Answer 1

#x_(1,2) = -2 +- 5#

To solve this quadratic by completing the square, you need to use the coefficient of the #x#-term to help you find a number that when added to both sides of the equation will allow you to write the left side as the square of a binomial.
More specifically, you need to divide the coefficient of the #x#-term by #2#, the nsquare the result
#(4/2)^2 = 2^2 = 4#

To obtain, add this term to each side of the equation.

#x^2 + 4x + 4 = 21 + 4#

Currently, the equation's left side can be expressed as

#x^2 + 4x + 4 = x^2 + 2 * (2) * x + (2)^2 = (x+2)^2#

This implies that you currently possess

#(x+2)^2 = 25#

Take each side's square root.

#sqrt((x+2)^2) = sqrt(25)#
#x+2 = +- 5#
#x = -2 +- 5 = {(x_1 = -2-5 = -7), (x_2 = -2 + 5 = 3) :}#
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Answer 2

To solve the quadratic equation by completing the square (x^2 + 4x = 21), follow these steps:

  1. Move the constant term to the other side of the equation: (x^2 + 4x - 21 = 0)

  2. Add and subtract the square of half the coefficient of the (x) term: (x^2 + 4x + 4 - 4 - 21 = 0)

  3. Rewrite the expression as a perfect square trinomial: ((x + 2)^2 - 25 = 0)

  4. Move the constant term to the other side of the equation: ((x + 2)^2 = 25)

  5. Take the square root of both sides (remembering to consider both positive and negative roots): (x + 2 = ±\sqrt{25})

  6. Solve for (x): (x + 2 = ±5)

  7. Subtract 2 from both sides: (x = -2 ± 5)

  8. The solutions are: (x = -2 + 5) and (x = -2 - 5)

    Which simplifies to: (x = 3) and (x = -7)

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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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