Respuesta :

Space

Answer:

[tex]\displaystyle x=\frac{-5 \pm \sqrt{29}}{4}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra I

  • Factoring
  • Standard Form: ax² + bx + c = 0
  • Quadratic Formula: [tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Step-by-step explanation:

Step 1: Define

4x² + 10x - 1 = 0

Step 2: Identify Variables

a = 4

b = 10

c = -1

Step 3: Find roots

  1. Substitute in variables [QF]:                    [tex]\displaystyle x=\frac{-10\pm\sqrt{10^2-4(4)(-1)} }{2(4)}[/tex]
  2. [√Radical] Exponents:                             [tex]\displaystyle x=\frac{-10\pm\sqrt{100-4(4)(-1)} }{2(4)}[/tex]
  3. [√Radical] Multiply:                                  [tex]\displaystyle x=\frac{-10\pm\sqrt{100+16}}{2(4)}[/tex]
  4. [√Radical] Add:                                        [tex]\displaystyle x=\frac{-10\pm\sqrt{116}}{2(4)}[/tex]
  5. [Fraction] Multiply:                                   [tex]\displaystyle x=\frac{-10\pm\sqrt{116}}{8}[/tex]
  6. [√Radical] Simplify:                                 [tex]\displaystyle x=\frac{-10\pm 2\sqrt{29}}{8}[/tex]
  7. [Fraction] Factor:                                     [tex]\displaystyle x=\frac{2(-5\pm \sqrt{29})}{8}[/tex]
  8. [Fraction] Simplify:                                  [tex]\displaystyle x=\frac{-5 \pm \sqrt{29}}{4}[/tex]

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