Math Problem Statement

One root of the equation x^2 - 81 = 0 is -9.

Solution

The given equation is:

x281=0x^2 - 81 = 0

To solve this equation, let's isolate x2x^2:

x2=81x^2 = 81

Taking the square root of both sides, we get:

x=±9x = \pm 9

Thus, the roots of the equation are x=9x = 9 and x=9x = -9.

Therefore, the statement "One root of the equation x281=0x^2 - 81 = 0 is -9" is True.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What are the steps to solve a quadratic equation using the square root method?
  2. How would you solve the equation x2100=0x^2 - 100 = 0?
  3. What is the significance of finding roots of an equation?
  4. How can you check if a value is truly a root of a given equation?
  5. How do you solve equations where the variable has an exponent greater than 2?

Tip: Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations

Formulas

x^2 = 81
x = ±√81

Theorems

Square Root Property

Suitable Grade Level

Grades 7-9