Question

now fill in the correct values. be extra careful with the signs. take note of what signs are already given to you. 2x² + 12x + 18 = 0 x = -() ± √(()² - ()()()) / ()

Explanation:

Step1: Recall Quadratic Formula

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) for a quadratic equation \( ax^2 + bx + c = 0 \).

Step2: Identify \( a \), \( b \), \( c \)

For the equation \( 2x^2 + 12x + 18 = 0 \), we have \( a = 2 \), \( b = 12 \), \( c = 18 \).

Step3: Substitute into Formula

Substitute \( a = 2 \), \( b = 12 \), \( c = 18 \) into the quadratic formula:
\( x = \frac{-(12) \pm \sqrt{(12)^2 - 4(2)(18)}}{2(2)} \)

Answer:

In the numerator's first box: \( 12 \), the square root's first box: \( 12 \), the exponent box: \( 2 \), the \( 4 \) box: \( 4 \), the next two boxes: \( 2 \) and \( 18 \) (in order), and in the denominator: \( 2 \) and \( 2 \) (in order). So filling the boxes:
\( x = \frac{-\boldsymbol{12} \pm \sqrt{\boldsymbol{12}^{\boldsymbol{2}} - \boldsymbol{4}(\boldsymbol{2})(\boldsymbol{18})}}{\boldsymbol{2}(\boldsymbol{2})} \)