(x+5)^2-20=0

2 min read Jun 17, 2024
(x+5)^2-20=0

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.

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