Question

question 1 (4 points) solve the quadratic using your preferred method. upload your handwritten work displaying how you solved the problem. $2x^2 + 20x = -58$

Explanation:

Step1: Rewrite in standard form

Add 58 to both sides:
$2x^2 + 20x + 58 = 0$
Divide by 2:
$x^2 + 10x + 29 = 0$

Step2: Use quadratic formula

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=1$, $b=10$, $c=29$.
Calculate discriminant:
$\Delta = 10^2 - 4(1)(29) = 100 - 116 = -16$

Step3: Compute roots with complex numbers

$\sqrt{-16}=4i$, substitute into formula:
$x=\frac{-10\pm4i}{2}$

Step4: Simplify the expression

Divide terms by 2:
$x = -5 \pm 2i$

Answer:

$x = -5 + 2i$ and $x = -5 - 2i$