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Answer:
Correct answer: x₁ = - 3/2 + i √7/2 or x₂ = - 3/2 - i √7/2
Step-by-step explanation:
We will first transform the given equation:
x² + 4x = x - 4 ⇒ x² + 4x - x + 4 = 0 ⇒ x² + 3x + 4 = 0
This equation has no solutions in the set of real numbers but it has in the set of complex numbers.
We will solve this equation as follows:
x² + 3x + 4 = x² + 2 · x · 3/2 + (3/2)² - (3/2)² + 4
the first three terms formed the square of the binomial
(x + 3/2)² - 9/4 + 4 = (x + 3/2)² - 9/4 + 16/4 = (x + 3/2)² + 7/4 =
= (x + 3/2)² - ( - 7/4) = (x + 3/2)² - (i √7/2)²
we gradually transformed the given equation and get the square difference
(x + 3/2)² - (i √7/2)² = (x + 3/2 - i √7/2) · (x + 3/2 - i √7/2)
(x + 3/2 - i √7/2) · (x + 3/2 - i √7/2) = 0 ⇒
x + 3/2 - i √7/2 = 0 or x + 3/2 + i √7/2 = 0 ⇒
x₁ = - 3/2 + i √7/2 or x₂ = - 3/2 - i √7/2
God is with you!!!
True cus I did that before
Answer:
see below
Step-by-step explanation:
Every vertex moves twice as far from the center of dilation as it is in the pre-image.
Perhaps the easiest image point to find is the one at lower left. In the pre-image it is 2 units left of the center of dilation, so the image point will be 2×2 = 4 units left of the center of dilation. It will be located at (-6, -2).
Other points on the image can be found either by reference to the center of dilation, or by reference to known image points. For example, the next point clockwise is 1 left and 4 up in the pre-image, so will be 2 left and 8 up from (-6, -2) in the image. That is, the pre-image point (-5, 2) becomes image point (-8, 6). You will note that (-5, 2) is 3 left and 4 up from the center of dilation, and that (-8, 6) is 6 left and 8 up from the center of dilation (twice as far away).