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Solving the Quadratic Equation: (x+5)^2 - 20 = 0
This article will guide you through the process of solving the quadratic equation (x+5)^2 - 20 = 0. We will use the following steps:
1. Expand the Square
First, we need to expand the squared term:
(x+5)^2 = (x+5)(x+5) = x^2 + 10x + 25
Now, our equation becomes:
x^2 + 10x + 25 - 20 = 0
2. Simplify the Equation
Combining like terms, we get:
x^2 + 10x + 5 = 0
3. Solve using the Quadratic Formula
The quadratic formula is used to solve equations of the form ax^2 + bx + c = 0. In our case, a = 1, b = 10, and c = 5.
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / 2a
Plugging in our values:
x = (-10 ± √(10^2 - 4 * 1 * 5)) / (2 * 1) x = (-10 ± √(80)) / 2 x = (-10 ± 4√5) / 2
4. Simplify the Solutions
We can simplify the solutions by dividing the numerator and denominator by 2:
x = -5 ± 2√5
Therefore, the solutions to the equation (x+5)^2 - 20 = 0 are:
x = -5 + 2√5 and x = -5 - 2√5
Conclusion
We have successfully solved the quadratic equation (x+5)^2 - 20 = 0 using the quadratic formula. The solutions are x = -5 + 2√5 and x = -5 - 2√5.