x^2-4x+12=0 Complete the square to solve for x.
Okay I know how to do up to here:
(-4/2)^2 -12=x^2-4x(-4/2)^2
2-12= x^2-4x+2
-10= DO I FACTOR IT?
Easist way always is to go and get the roots:
(-b + sqrt(b^2 - 4ac)) / 2a
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x^2 -4x +12 = 0
a= 1, b=-4 c = 12
(-(-4) + sqrt(16 - 4*12)) / 2
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(4 + sqrt(-32))/2
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4 + sqrt(i^2 * 16 *2))/2
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note : i^2 = -1
(4 + i 4 sqrt(2))/2
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Ans:
2+ 2i sqrt(2)
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are the two roots
Hope this helps Christine!
No need to factor it at this point. To complete the square, we want to rewrite the equation in the form (x - h)^2 = k, where h and k are constants.
In this case, we have: x^2 - 4x + 12 = 0
First, let's move the constant term (12) to the other side of the equation:
x^2 - 4x = -12
Next, we need to "complete the square" by adding the square of half of the coefficient of x to both sides of the equation. The coefficient of x is -4, so the value we need to add is (half of -4)^2 = (-2)^2 = 4.
Adding 4 to both sides of the equation, we get:
x^2 - 4x + 4 = -12 + 4
x^2 - 4x + 4 = -8
Now, we can write the left side of the equation as a perfect square:
(x - 2)^2 = -8
Finally, to solve for x, we take the square root of both sides:
sqrt((x - 2)^2) = sqrt(-8)
x - 2 = ±sqrt(-8)
Since sqrt(-8) is not a real number, this equation does not have any real solutions. However, if you are asked to find the complex solutions, you can continue by simplifying sqrt(-8) as 2i*sqrt(2):
x - 2 = ±2i*sqrt(2)
Solving for x:
x = 2 ± 2i*sqrt(2)
Therefore, the solutions to the equation are x = 2 + 2i*sqrt(2) and x = 2 - 2i*sqrt(2).
To complete the square and solve for x, follow the steps below:
1. Start with the equation: x^2 - 4x + 12 = 0.
2. Shift the constant term (12 in this case) to the right side of the equation: x^2 - 4x = -12.
3. Divide the coefficient of x by 2, square the result, and add it to both sides of the equation: x^2 - 4x + (4/2)^2 = -12 + (4/2)^2.
Simplifying this gives: x^2 - 4x + 4 = -12 + 4.
4. Simplify further: x^2 - 4x + 4 = -8.
5. Rewrite the left side as a perfect square trinomial: (x - 2)^2 = -8.
6. Take the square root of both sides: sqrt((x - 2)^2) = sqrt(-8).
This gives: x - 2 = ±√(-8).
7. Since we have the square root of a negative number, we can express it in terms of 'i', the imaginary unit.
We can rewrite -8 as 8 * -1, so sqrt(-8) becomes √(8 * -1) = √8 * √(-1) = 2√2 * i.
8. Now we have: x - 2 = ±2√2 * i.
9. Add 2 to both sides to isolate x: x = 2 ± 2√2 * i.
Hence, the solutions to the equation x^2 - 4x + 12 = 0, after completing the square, are x = 2 + 2√2 * i and x = 2 - 2√2 * i.
x^2 - 4x = -12
x^2 - 4x + 4 = -12 + 4
(x-2)^2 = -8
x-2 = ± √-8 , but √-8 = 2√2 √-1 = 2i√2
x = 2 ± 2i√2