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Okay, we've reached the final stretch! We have **x = (-4 ± 10i) / 2**. To simplify this, we'll divide both the real part (-4) and the imaginary part (10i) by 2. So, **-4 / 2 = -2** and **10i / 2 = 5i**. This gives us two solutions: **x = -2 + 5i** and **x = -2 - 5i**. These are our complex solutions! Notice that they come in a conjugate pair: -2 + 5i and -2 - 5i. Complex solutions of quadratic equations always come in conjugate pairs when the coefficients (a, b, and c) are real numbers. This is a handy check to make sure you haven't made a mistake. So, what do these solutions actually mean? Well, graphically, it means that the parabola represented by **x² + 4x + 29 = 0** doesn't intersect the x-axis. It floats either entirely above or entirely below the x-axis. In this case, since 'a' is positive (a = 1), the parabola opens upwards and sits entirely above the x-axis. Congratulations! You've successfully solved a quadratic equation with complex solutions. You’ve navigated through the quadratic formula, handled the imaginary unit 'i', and found the complex roots. This is a fantastic achievement, guys! You've added a valuable tool to your math toolbox.
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