(x+5)^2-18=0

2 min read Jun 17, 2024

Solving the Quadratic Equation: (x+5)^2 - 18 = 0

This article will guide you through the steps of solving the quadratic equation (x+5)^2 - 18 = 0.

Understanding the Equation

The given equation is a quadratic equation, which means it involves a variable raised to the power of two. This equation is in a slightly disguised form, but we can easily transform it into the standard quadratic equation form: ax^2 + bx + c = 0.

Steps to Solve

Expand the squared term:
(x+5)^2 = (x+5)(x+5) = x^2 + 10x + 25
Rewrite the equation: x^2 + 10x + 25 - 18 = 0
Simplify the equation: x^2 + 10x + 7 = 0
Solve using the quadratic formula: The quadratic formula is used to find the roots (solutions) of a quadratic equation: x = (-b ± √(b^2 - 4ac)) / 2a Where a = 1, b = 10, and c = 7 from our simplified equation.
Substitute the values into the formula: x = (-10 ± √(10^2 - 4 * 1 * 7)) / (2 * 1) x = (-10 ± √(68)) / 2 x = (-10 ± 2√17) / 2
Simplify the solutions: x = -5 ± √17

Solutions

Therefore, the solutions to the quadratic equation (x+5)^2 - 18 = 0 are:

x = -5 + √17
x = -5 - √17

Conclusion

By expanding, simplifying, and applying the quadratic formula, we successfully solved the equation (x+5)^2 - 18 = 0 and obtained the two distinct solutions.