Question

what are the solutions of the equation $2x^2 + 4x + 10 = 0$? if it has complex solutions, write them in the form $(a pm bi)$. use the keypad to enter the answer in the box. additional symbols can be found using the drop - down arrows at the top of the keypad. for this equation, the solutions of the equation are $x = square$ and $x = square$.

Explanation:

Step1: Identify coefficients

For $2x^2 + 4x + 10 = 0$, $a=2$, $b=4$, $c=10$

Step2: Use quadratic formula

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

Step3: Calculate discriminant

$\Delta = 4^2 - 4(2)(10) = 16 - 80 = -64$

Step4: Compute square root of discriminant

$\sqrt{-64} = 8i$

Step5: Substitute into formula

$x=\frac{-4\pm8i}{2(2)}=\frac{-4\pm8i}{4}$

Step6: Simplify the expression

$x=-1\pm2i$

Answer:

$x = -1 + 2i$ and $x = -1 - 2i$