Solve the equation using square roots. Select the solution(s).
[tex](x+3)^2=0[/tex]
Answer (1)
Take the square root of both sides of the equation: ( x + 3 ) 2 = 0 .
Simplify the equation to x + 3 = 0 .
Solve for x by subtracting 3 from both sides: x = − 3 .
The solution to the equation is − 3 .
Explanation
Understanding the Problem We are given the equation ( x + 3 ) 2 = 0 and asked to solve for x using square roots.
Taking the Square Root To solve the equation, we take the square root of both sides: ( x + 3 ) 2 = 0 This simplifies to: x + 3 = 0
Solving for x Now, we isolate x by subtracting 3 from both sides of the equation: x + 3 − 3 = 0 − 3 x = − 3
Final Answer Therefore, the solution to the equation ( x + 3 ) 2 = 0 is x = − 3 .
Examples
Consider a scenario where you're designing a square garden bed. The area of the garden bed is represented by the equation ( x + 3 ) 2 = 0 , where x is a variable related to the dimensions. Solving this equation helps you determine the specific value of x that makes the area zero, indicating a point where the design might need adjustment or has a unique characteristic. This type of problem is applicable in various design and engineering contexts where finding specific values that satisfy certain conditions is crucial.
