Final answer:
The negative solution of the quadratic equation 3x^2 - 5 = -10x, rounded to the nearest hundredth, is x = -3.78.
Step-by-step explanation:
To find the negative solution of the quadratic equation 3x^2 - 5 = -10x, we need to first put the equation in standard form. By adding 10x to both sides of the equation, we get 3x^2 + 10x - 5 = 0. Now, we can use the quadratic formula x = (-b ± √(b^2-4ac))/(2a) to find the values of x.
For our equation, a = 3, b = 10, and c = -5. Plugging these values into the quadratic formula:
x = [-(10) ± √((10)^2 - 4(3)(-5))]/(2(3))
x = [-10 ± √(100 + 60)]/6
x = [-10 ± √160]/6
x = [-10 ± 12.65]/6
We have two solutions here, and since we are looking for the negative solution, we choose -10 - 12.65 = -22.65, and divide by 6:
x = -22.65/6
x = -3.78 (rounded to the nearest hundredth)
Therefore, the negative solution of the equation 3x^2 + 10x - 5 = 0, rounded to the nearest hundredth, is x = -3.78.