Questions: Solve using the quadratic formula: -6x^2 - 4x + 2 = 0 Select the correct answer below: (-4 ± 8)/-12 (4 ± 2√10)/-6 (4 ± 2√10)/-12 (4 ± 2√7)/-12 (4 ± 8)/-6 (4+8)/-12

Solution Steps

To solve the quadratic equation \(-6x^2 - 4x + 2 = 0\) using the quadratic formula, we identify the coefficients \(a = -6\), \(b = -4\), and \(c = 2\). The quadratic formula is given by:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

We will substitute the values of \(a\), \(b\), and \(c\) into this formula to find the solutions for \(x\).

The given quadratic equation is

\[ -6x^2 - 4x + 2 = 0 \]

From this equation, we identify the coefficients as follows:

• \(a = -6\)
• \(b = -4\)
• \(c = 2\)

We calculate the discriminant \(D\) using the formula:

\[ D = b^2 - 4ac \]

Substituting the values of \(a\), \(b\), and \(c\):

\[ D = (-4)^2 - 4 \cdot (-6) \cdot 2 = 16 + 48 = 64 \]

Using the quadratic formula

\[ x = \frac{-b \pm \sqrt{D}}{2a} \]

we substitute \(b\) and \(D\):

\[ x = \frac{-(-4) \pm \sqrt{64}}{2 \cdot (-6)} = \frac{4 \pm 8}{-12} \]

Calculating the two possible values for \(x\):

1. For \(x_1\):

\[ x_1 = \frac{4 + 8}{-12} = \frac{12}{-12} = -1 \]

2. For \(x_2\):

\[ x_2 = \frac{4 - 8}{-12} = \frac{-4}{-12} = \frac{1}{3} \]

Final Answer