Question

Nine more than seven times a number, n, gives the same value as one more than the square of the number. Write an equation and solve it to find the number.

Answer 1

7n + 9 = n² + 1

n = -1, 8

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

Algebra I

• Factoring
• Solving quadratics

Explanation:

Step 1: Set up Equation

"Nine more" is + 9

"Seven times a number" is 7n

"One more" is + 1

"Square of the [same] number" is n²

7n + 9 = n² + 1

Step 2: Solve for n

1. Subtract 7n on both sides: 9 = n² - 7n + 1
2. Subtract 9 on both sides: 0 = n² - 7n - 8
3. Factor quadratic: 0 = (n - 8)(n + 1)
4. Solve roots: n = -1, 8