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  1. [tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]

    General Formulas and Concepts:


    Order of Operations: BPEMDAS

    Alg I

    Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]√-1 is imaginary number i

    Step-by-step explanation:

    Step 1: Define

    3x² - 4x + 4 = 0

    a = 3

    b = -4

    c = 4

    Step 2: Find roots

    Substitute:                    [tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]Simplify:                        [tex]x=\frac{4\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]Evaluate:                       [tex]x=\frac{4\pm\sqrt{16-4(3)(4)} }{2(3)}[/tex]Multiply:                        [tex]x=\frac{4\pm\sqrt{16-48} }{6}[/tex]Subtract:                       [tex]x=\frac{4\pm\sqrt{-32} }{6}[/tex]Factor:                          [tex]x=\frac{4\pm\sqrt{-1} \sqrt{32} }{6}[/tex]Simplify:                       [tex]x=\frac{4\pm4i\sqrt{2} }{6}[/tex]Factor:                          [tex]x=\frac{4(1\pm i\sqrt{2} )}{6}[/tex]Simplify:                       [tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]

  2. hey there!

    if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

    500 ÷ 6 = [tex]83.\overline3[/tex]

    she needs to save at least this amount each month, so we should use this symbol: ≥

    let x be the amount she saves each month.

    your final answer is x ≥ [tex]83.\overline3[/tex]

    hope this !

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