How do you solve #x^2-12x+20=0# by completing the square?

Answer 1

#x_(1,2) = 6 +- 4#

First, enter your quadratic in the appropriate form.

#color(blue)(x^2 + b/ax = -c/a)#
This can be done by adding #-20# to both sides of the equation
#x^2 - 12x + color(red)(cancel(color(black)(20))) - color(red)(cancel(color(black)(20))) = 0 - 20#
#x^2 - 12x = -20#
Now use the coefficient of the #x#-term to find a term 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 this coefficient by #2# and square the result.
#((-12)/2)^2 = (-6)^2 = 36#
So, add #36# to both sides of the equation to get
#x^2 - 12x + 36 = -20 + 36#

This allows us to write the left side of the equation as

#x^2 - 2 * (6) * x + (6)^2 = (x-6)^2#

This indicates that you've

#(x-6)^2 = 16#

Get the answer by taking the square root of each side of the equation.

#sqrt((x-6)^2) = sqrt(16)#
#x-6 = +- 4#
#x = 6 +- 4 = {(x_1 = 6 + 4 = color(green)(10)), (x_2 = 6 - 4 = color(green)(2)):}#
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Answer 2

To solve the quadratic equation (x^2 - 12x + 20 = 0) by completing the square, follow these steps:

  1. Move the constant term to the other side of the equation: (x^2 - 12x = -20)

  2. To complete the square, halve the coefficient of (x), square it, and add it to both sides of the equation: Add ((\frac{12}{2})^2 = 36) to both sides: (x^2 - 12x + 36 = -20 + 36)

  3. Simplify: ((x - 6)^2 = 16)

  4. Take the square root of both sides: (x - 6 = \pm \sqrt{16})

  5. Solve for (x): (x - 6 = \pm 4) (x = 6 \pm 4)

  6. Simplify: (x = 10) or (x = 2)

So, the solutions to the equation (x^2 - 12x + 20 = 0) by completing the square are (x = 10) and (x = 2).

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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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