Final answer:
To solve the quadratic equation 5x² + 45x + 90 = 0, you can use the quadratic formula. The solutions for x are x = -3 or x = -6.
Step-by-step explanation:
To solve the quadratic equation 5x² + 45x + 90 = 0, we can use the quadratic formula. The quadratic formula states that x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
In this equation, a = 5, b = 45, and c = 90. Substituting these values into the quadratic formula, we get:
x = (-45 ± √(45^2 - 4 * 5 * 90)) / (2 * 5)
Simplifying further, we have:
x = (-45 ± √(2025 - 1800)) / 10
x = (-45 ± √225) / 10
x = (-45 ± 15) / 10
So the solutions for x are x = (-45 + 15) / 10 and x = (-45 - 15) / 10. Therefore, x = -3 or x = -6.