Question

solve the quadratic equation.
\\(x^2 + 6x + 18 = 0\\)
write one exact, simplified solution in each box. you can add or remove boxes. if a solution is not a real number, write it in the form \\(a + bi\\) or \\(a - bi\\), where \\(a\\) and \\(b\\) are real numbers.

Explanation:

Step1: Identify coefficients

For \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = 6\), \(c = 18\).

Step2: Use quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Calculate discriminant: \(b^2 - 4ac = 6^2 - 4(1)(18)=36 - 72=-36\)

Step3: Substitute into formula

\(x=\frac{-6\pm\sqrt{-36}}{2(1)}=\frac{-6\pm6i}{2}\)
Simplify: \(x=-3\pm3i\)

Answer:

\(-3 + 3i\), \(-3 - 3i\)