%5E2%3D0.jpeg "(x+5)^2=0")
Solving the Equation (x+5)^2 = 0
The equation (x+5)^2 = 0 is a simple quadratic equation that can be solved using a few basic steps.
Understanding the Equation
The equation (x+5)^2 = 0 represents a perfect square trinomial. This means that the expression on the left side of the equation is the result of squaring a binomial, in this case, (x+5).
Solving for x
To solve for x, we can follow these steps:
- Take the square root of both sides: √(x+5)^2 = √0
- Simplify: This gives us x+5 = 0
- Isolate x: Subtract 5 from both sides to get x = -5
Solution and Verification
Therefore, the solution to the equation (x+5)^2 = 0 is x = -5.
We can verify this solution by substituting x = -5 back into the original equation:
(-5 + 5)^2 = 0
0^2 = 0
This confirms that our solution is correct.
Graphing the Equation
The equation (x+5)^2 = 0 represents a parabola that intersects the x-axis at the point (-5, 0). Since the square of any real number is always non-negative, the parabola only touches the x-axis at this single point. This indicates that the equation has a double root, meaning the solution x = -5 occurs twice.
Conclusion
The equation (x+5)^2 = 0 has a single solution, x = -5, which is a double root. This solution can be found by taking the square root of both sides of the equation and simplifying. Understanding the concept of perfect square trinomials and double roots can be helpful in solving similar quadratic equations.