Question

Choose a method to solve the quadratic equation. Explain your choice. $$x^{2}+6 x-55=0$$

Short answer

The solutions to the equation \(x^{2}+6 x-55=0\) are \(x = 5\) and \(x = -11\).

Step-by-step solution

Identify the Equation Type

First, identify that the equation is a quadratic equation, which can be represented in general form \( ax^2 + bx + c = 0 \). The value of \(a\) is 1, \(b\) is 6, and \(c\) is -55.

Factoring the Quadratic Equation

The quadratic equation can be factored by finding two numbers that multiply to \(-55\) (the product of \(a\) and \(c\)) and add to \(6\) (the value of \(b\)). These two numbers are \(-5\) and \(11\). So, the factored form of the equation is: \( (x - 5)(x + 11) = 0 \).

Find the Roots of the Equation

To find the solutions, or roots, of the equation, set each factor equal to zero and solve for \(x\): \( (x - 5) = 0 ---> x = 5 \) \( (x + 11) = 0 ---> x = -11 \).