Question

eoc style question what are the solutions of the equation $x^2 + 6x - 9 = 0$? $3pm 6sqrt{2}$ $-3pm 6sqrt{2}$ $3pm 3sqrt{2}$ $-3pm 3sqrt{2}$

Explanation:

Step1: Identify the quadratic formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are given by \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). In the equation \(x^2+6x - 9 = 0\), we have \(a = 1\), \(b = 6\), and \(c=-9\).

Step2: Calculate the discriminant

The discriminant \(D=b^2 - 4ac\). Substituting the values, we get \(D=(6)^2-4\times1\times(-9)=36 + 36=72\).

Step3: Substitute into the quadratic formula

Now, \(x=\frac{-6\pm\sqrt{72}}{2\times1}\). Simplify \(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\). So, \(x=\frac{-6\pm6\sqrt{2}}{2}\).

Step4: Simplify the expression

Divide numerator and denominator by 2: \(x=-3\pm3\sqrt{2}\).

Answer:

\(-3\pm3\sqrt{2}\) (corresponding to the option with this expression)