Math Problem Statement

Solve x^2 = 121 and x^2 = 64

Solution

The homework asks you to solve two equations:

  1. x2=121x^2 = 121
  2. x2=64x^2 = 64

Solution for x2=121x^2 = 121:

To solve for xx, take the square root of both sides: x=±121x = \pm \sqrt{121} x=±11x = \pm 11 So, the solutions are x=11x = 11 and x=11x = -11.

Solution for x2=64x^2 = 64:

Similarly, take the square root of both sides: x=±64x = \pm \sqrt{64} x=±8x = \pm 8 So, the solutions are x=8x = 8 and x=8x = -8.

Would you like further details on the method or have any additional questions?

Here are some related questions to explore:

  1. What is the general method for solving quadratic equations like x2=cx^2 = c?
  2. How do we know when to include both positive and negative solutions?
  3. Can you solve equations like x2=49x^2 = -49? Why or why not?
  4. What happens if the equation is x2=0x^2 = 0?
  5. How can you apply this technique to more complex equations?

Tip: Always remember that for equations involving squares, there are typically two solutions—one positive and one negative—unless the equation equals zero.

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Roots
Quadratic Equations

Formulas

x^2 = c → x = ±√c

Theorems

Square Root Theorem

Suitable Grade Level

Grades 6-8