The answer is option c, but if you need an explanation refer to the attachment below -
Answer:
![x=\frac{1\pm i\sqrt{11}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%5Cpm%20i%5Csqrt%7B11%7D%7D%7B4%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Standard Form: ax² + bx + c = 0
- Quadratic Formula:
![x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%20%7D%7B2a%7D)
<u>Algebra II</u>
Step-by-step explanation:
<u>Step 1: Define Equation</u>
4x² - 2x + 3 = 0
<u>Step 2: Identify Variables</u>
a = 4
b = -2
c = 3
<u>Step 3: Solve for </u><em><u>x</u></em>
- Substitute [Quad Formula]:
![x=\frac{2\pm\sqrt{(-2)^2-4(4)(3)} }{2(4)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%5Csqrt%7B%28-2%29%5E2-4%284%29%283%29%7D%20%7D%7B2%284%29%7D)
- Evaluate Exponents:
![x=\frac{2\pm\sqrt{4-4(4)(3)} }{2(4)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%5Csqrt%7B4-4%284%29%283%29%7D%20%7D%7B2%284%29%7D)
- Evaluate Multiplication:
![x=\frac{2\pm\sqrt{4-48} }{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%5Csqrt%7B4-48%7D%20%7D%7B8%7D)
- Evaluate Subtraction:
![x=\frac{2\pm\sqrt{-44} }{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%5Csqrt%7B-44%7D%20%7D%7B8%7D)
- Factor Radical:
![x=\frac{2\pm\sqrt{-1} \sqrt{44} }{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%5Csqrt%7B-1%7D%20%5Csqrt%7B44%7D%20%7D%7B8%7D)
- Simplify Radicals:
![x=\frac{2\pm 2i\sqrt{11} }{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%202i%5Csqrt%7B11%7D%20%7D%7B8%7D)
- Factor Numerator GCF:
![x=\frac{2(1\pm i\sqrt{11}) }{8}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%281%5Cpm%20i%5Csqrt%7B11%7D%29%20%7D%7B8%7D)
- Simplify:
![x=\frac{1\pm i\sqrt{11}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%5Cpm%20i%5Csqrt%7B11%7D%7D%7B4%7D)
Answer:
The correct answer is option C. x² - 4
Step-by-step explanation:
Area of rectangle = Length * Width
It is given that ,
The length of a side of a rectangle is 2 units less than a number, and the width is 4 units more than the length.
Let 'x' be the number
Length of rectangle = x - 2
Width = Length + 4 = x - 2 + 4 = x + 2
<u>To find the area of rectangle</u>
Area = Length * Width
Area = (x - 2)*(x + 2) = x² - 4
Therefore option C. x² - 4 is the correct answer