Question

Analyze the diagram below and complete the instructions that follow.

Answer 1

Answer:

x = 6

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  

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtract Property of Equality

Algebra I

• Terms/Coefficients/Degrees
• Expand by FOIL (First Outside Inside Last)
• Factoring
• Multiple Roots

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

• a is a leg
• b is another leg
• c is the hypotenuse

Step-by-step explanation:

Step 1: Identify

a = x + 3

b = x

c = √117

Step 2: Solve for x

1. Substitute [PT]:                                                                                                (x + 3)² + x² = (√117)²
2. Expand [FOIL]:                                                                                                 x² + 6x + 9 + x² = (√117)²
3. Combine like terms:                                                                                       2x² + 6x + 9 = (√117)²
4. Exponents:                                                                                                      2x² + 6x + 9 = 117
5. [SPE] Subtract 117 on both sides:                                                                    2x² + 6x - 108 = 0
6. Factor out GCF:                                                                                               2(x² + 3x - 54) = 0
7. [DPE] Divide 2 on both sides:                                                                         x² + 3x - 54 = 0
8. Factor Quadratic:                                                                                            (x - 6)(x + 9) = 0
9. Solve roots/solve x:                                                                                         x = -9, 6

Since we are dealing with positive values, we can disregard the negative root.

∴ x = 6