Question

question 11 (3 points)

solve. express as exact answers.

\\2x^2 + 12x = -5\\

Explanation:

Write the equation in standard form

We rewrite the equation in standard form \(ax^2 + bx + c = 0\).

$$ 2x^2 + 12x + 5 = 0 $$

Apply the quadratic formula

We identify the coefficients \(a = 2\), \(b = 12\), and \(c = 5\).

$$ x = \frac{-12 \pm \sqrt{12^2 - 4(2)(5)}}{2(2)} $$

$$ x = \frac{-12 \pm \sqrt{144 - 40}}{4} $$

$$ x = \frac{-12 \pm \sqrt{104}}{4} $$

Simplify the radical expression

Using the Simplifying Radicals knowledge point

$$ \sqrt{104} = \sqrt{4 \times 26} = 2\sqrt{26} $$

Reduce the final fraction

We substitute the simplified radical back into the expression and divide.

$$ x = \frac{-12 \pm 2\sqrt{26}}{4} $$

$$ x = \frac{2(-6 \pm \sqrt{26})}{4} $$

$$ x = \frac{-6 \pm \sqrt{26}}{2} $$

Answer:

\(x = \frac{-6 \pm \sqrt{26}}{2}\)