Question

What is the positive value of “x”?
x(x+5)=387
Hint: Use the quadratic formula

Answer 1

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…

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....

Answer 2

`\displaystyle x=(-5+11√(13))/(2)`

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:
  `\displaystyle x=(-b\pm√(b^2-4ac) )/(2a)`

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]:
   `\displaystyle x=(-5\pm√(5^2-4(1)(-387)))/(2(1))`
2. [√Radical] Evaluate exponents:
   `\displaystyle x=(-5\pm√(25-4(1)(-387)))/(2(1))`
3. [√Radical] Multiply:
   `\displaystyle x=(-5\pm√(25+1548))/(2(1))`
4. [√Radical] Add:
   `\displaystyle x=(-5\pm√(1573))/(2(1))`
5. [Fraction - Denominator] Multiply:
   `\displaystyle x=(-5\pm√(1573))/(2)`
6. [Fraction - √Radical] Simplify:
   `\displaystyle x=(-5\pm 11√(13))/(2)`