How do you solve using completing the square method #y=x^2-12x +40#?
Solution:
Number(x^2–12x +36)–36+40=0# or
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
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To solve the equation using completing the square method, follow these steps:
- Rewrite the equation in the form y = (x - h)^2 + k by completing the square.
- Find the value of h by taking half of the coefficient of x and squaring it.
- Find the value of k by adding the square of half the coefficient of x to both sides of the equation.
- Rewrite the equation in the form y = (x - h)^2 + k.
- Identify the vertex coordinates (h, k).
- Use the vertex coordinates to graph the parabola.
Applying these steps to the equation y = x^2 - 12x + 40, we have:
- y = (x^2 - 12x) + 40
- Take half of the coefficient of x and square it: (-12/2)^2 = 36.
- Add 36 to both sides of the equation: y + 36 = (x^2 - 12x + 36) + 40.
- Rewrite the equation: y + 36 = (x - 6)^2 + 40.
- Identify the vertex coordinates: (6, 40 - 36) = (6, 4).
- The vertex of the parabola is at (6, 4).
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To solve the equation ( y = x^2 - 12x + 40 ) using the completing the square method, follow these steps:
- Write the equation in the form ( y = (x - h)^2 + k ).
- Complete the square for the quadratic term ( x^2 - 12x ).
- Add or subtract the necessary constant to both sides of the equation to maintain equality.
The completing the square process is as follows:
- ( y = x^2 - 12x + 40 )
- ( y = (x^2 - 12x + \underline{36}) - 36 + 40 ) (Adding and subtracting ( 36 ) to complete the square)
- ( y = (x - 6)^2 + 4 )
Therefore, the solution is ( y = (x - 6)^2 + 4 ).
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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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