Respuesta :

Answer:

x= −5−11√13/2, −5+11√13/2

Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.

Exact Form:

x= −5−11√13/2, −5+11√13/2

Decimal Form:

x=17.33053201…,

−22.33053201…

Step-by-step explanation:

x(x+5)=387

Simplify

x(x+5).

x^2+5x=387

Subtract 387 from both sides of the equation.

x^2+5x−387=0

Use the quadratic formula to find the solutions.

−b±√b^2−4(ac)/2a

Substitute the values a=1, b=5, and c= −387 into the quadratic formula and solve for x.−5±√5^2−4⋅(1⋅−387)/2⋅1

Simplify.

x=−5±11√13/2

The final answer is the combination of both solutions.

x=−5−11√13/2, −5+11√13/2

The result can be shown in multiple forms.

Exact Form:

x=−5−11√13/2,−5+11√13/2

Decimal Form:

x=17.33053201…,

−22.33053201…

Hope it is helpful....

Space

Answer:

[tex]\displaystyle x=\frac{-5+11\sqrt{13}}{2}[/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  

Distributive Property

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Algebra I

  • 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

x(x + 5) = 387

Step 2: Identify Variables

Rewrite

  1. [Distributive Property] Distribute x:                                                               x² + 5x = 387
  2. [Subtraction Property of Equality] Subtract 387 on both sides:                  x² + 5x - 387 = 0
  3. Part:                                                                                                                 a = 1, b = 5, c = -387

Step 3: Solve for x

  1. Substitute in variables [Quadratic Formula]:                                                [tex]\displaystyle x=\frac{-5\pm\sqrt{5^2-4(1)(-387)}}{2(1)}[/tex]
  2. [√Radical] Evaluate exponents:                                                                    [tex]\displaystyle x=\frac{-5\pm\sqrt{25-4(1)(-387)}}{2(1)}[/tex]
  3. [√Radical] Multiply:                                                                                         [tex]\displaystyle x=\frac{-5\pm\sqrt{25+1548}}{2(1)}[/tex]
  4. [√Radical] Add:                                                                                               [tex]\displaystyle x=\frac{-5\pm\sqrt{1573}}{2(1)}[/tex]
  5. [Fraction - Denominator] Multiply:                                                                  [tex]\displaystyle x=\frac{-5\pm\sqrt{1573}}{2}[/tex]
  6. [Fraction - √Radical] Simplify:                                                                        [tex]\displaystyle x=\frac{-5\pm 11\sqrt{13}}{2}[/tex]

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