Question

lets simplify. 2x² + 12x + 18 = 0 x = (□ ± √□)/□

Explanation:

Step1: Simplify the equation

First, divide the entire quadratic equation \(2x^{2}+12x + 18=0\) by 2 to simplify it. We get \(x^{2}+6x + 9 = 0\). In the standard quadratic form \(ax^{2}+bx + c=0\), here \(a = 1\), \(b=6\), \(c = 9\).

Step2: Use the quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). Substitute \(a = 1\), \(b = 6\), \(c=9\) into the formula. First, calculate the discriminant \(b^{2}-4ac=(6)^{2}-4\times1\times9=36 - 36=0\). Then, \(-b=- 6\), \(2a = 2\times1 = 2\). So we have \(x=\frac{-6\pm\sqrt{0}}{2}\).

Answer:

\(x=\frac{-6\pm\sqrt{0}}{2}\) (So the numbers in the boxes are \(-6\), \(0\), \(2\) respectively)