Question

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

Answer 1

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....

Answer 2

Answer:

$\displaystyle x=\frac{-5+11\sqrt{13}}{2}$

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: $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

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