Question

e quadratic formula.
b. $2x^2 + 4x + 7 = 0$

Explanation:

Step1: Identify coefficients

For $2x^2 + 4x + 7 = 0$, $a=2$, $b=4$, $c=7$

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

$\Delta = b^2 - 4ac = 4^2 - 4(2)(7) = 16 - 56 = -40$

Step4: Substitute into formula

$x = \frac{-4 \pm \sqrt{-40}}{2(2)} = \frac{-4 \pm 2i\sqrt{10}}{4}$

Step5: Simplify the expression

$x = \frac{-2 \pm i\sqrt{10}}{2}$

Answer:

$x = \frac{-2 + i\sqrt{10}}{2}$ and $x = \frac{-2 - i\sqrt{10}}{2}$