How do you solve using completing the square method #y=x^2-12x +40#?

Answer 1

Solution: # x= 6+2i and x= 6-2i#

Suppose #x^2–12x+40 = 0 or #(x^2–12x)+40 = 0#.

Number(x^2–12x +36)–36+40=0# or

(x-6)=+-sqrt (-4)# or #(x-6)^2=-4

If i^2=-1, then #(x-6)=+-sqrt (4i^2) or

x= 6+2i and x= 6-2i#; x-6 =+-2i or x = 6+- 2i

The answers are #x= 6+2i and #x= 6-2i# [Ans].
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Answer 2

To solve the equation using completing the square method, follow these steps:

  1. Rewrite the equation in the form y = (x - h)^2 + k by completing the square.
  2. Find the value of h by taking half of the coefficient of x and squaring it.
  3. Find the value of k by adding the square of half the coefficient of x to both sides of the equation.
  4. Rewrite the equation in the form y = (x - h)^2 + k.
  5. Identify the vertex coordinates (h, k).
  6. Use the vertex coordinates to graph the parabola.

Applying these steps to the equation y = x^2 - 12x + 40, we have:

  1. y = (x^2 - 12x) + 40
  2. Take half of the coefficient of x and square it: (-12/2)^2 = 36.
  3. Add 36 to both sides of the equation: y + 36 = (x^2 - 12x + 36) + 40.
  4. Rewrite the equation: y + 36 = (x - 6)^2 + 40.
  5. Identify the vertex coordinates: (6, 40 - 36) = (6, 4).
  6. The vertex of the parabola is at (6, 4).
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Answer 3

To solve the equation ( y = x^2 - 12x + 40 ) using the completing the square method, follow these steps:

  1. Write the equation in the form ( y = (x - h)^2 + k ).
  2. Complete the square for the quadratic term ( x^2 - 12x ).
  3. Add or subtract the necessary constant to both sides of the equation to maintain equality.

The completing the square process is as follows:

  1. ( y = x^2 - 12x + 40 )
  2. ( y = (x^2 - 12x + \underline{36}) - 36 + 40 ) (Adding and subtracting ( 36 ) to complete the square)
  3. ( y = (x - 6)^2 + 4 )

Therefore, the solution is ( y = (x - 6)^2 + 4 ).

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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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