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mash [69]
2 years ago
13

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 so

lve it to find the number.
Mathematics
1 answer:
Maru [420]2 years ago
4 0

Answer:

7n + 9 = n² + 1

n = -1, 8

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Algebra I</u>

  • Factoring
  • Solving quadratics

Step-by-step explanation:

<u>Step 1: Set up Equation</u>

"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

<u>Step 2: Solve for </u><em><u>n</u></em>

  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
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