Question

Analyze the diagram below and complete the instructions that follow.

1117
X
x + 3
Find the value of x.

Answer 1

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

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