solve the quadratic equation.\n4x² + 4x + 5 = 0\nwrite one exact solution in each box. you can add or remove…

Explanation:

Step1: Identify coefficients

For the quadratic equation $4x^{2}+4x + 5=0$, we have $a = 4$, $b = 4$, $c = 5$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(4)^{2}-4\times4\times5=16 - 80=- 64$.

Step3: Use the quadratic - formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Since $\Delta=-64$, we have $x=\frac{-4\pm\sqrt{-64}}{2\times4}=\frac{-4\pm8i}{8}$.

Step4: Simplify the solutions

$x=\frac{-4 + 8i}{8}=-\frac{1}{2}+i$ and $x=\frac{-4 - 8i}{8}=-\frac{1}{2}-i$.

Answer:

$-\frac{1}{2}+i$, $-\frac{1}{2}-i$