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(x+5)^2=4

2 min read Jun 17, 2024
(x+5)^2=4

Solving the Equation (x+5)^2 = 4

This equation represents a quadratic equation in disguise. Let's break down how to solve it:

Understanding the Equation

  • The Square: The expression (x+5)^2 means that we are squaring the entire term (x+5).
  • The Goal: Our goal is to find the value(s) of 'x' that satisfy the equation.

Solving for x

  1. Take the square root of both sides:

    √((x+5)^2) = √4

    This gives us:

    x+5 = ±2

  2. Isolate x:

    • For the positive solution:
      x + 5 = 2
x = 2 - 5 
x = -3
    • For the negative solution:
      x + 5 = -2
x = -2 - 5
x = -7

Solutions

Therefore, the solutions to the equation (x+5)^2 = 4 are x = -3 and x = -7.

Verification

We can verify our solutions by substituting them back into the original equation:

  • For x = -3: (-3 + 5)^2 = 2^2 = 4. True
  • For x = -7: (-7 + 5)^2 = (-2)^2 = 4. True

Both solutions satisfy the original equation.

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