Question

What is the solution to the quadratic equation x² + 10x = 75 when rounded to the nearest tenth?

a) x = 5.3
b) x = 4.2
c) x = 3.8
d) x = 4.8

Answer 1

The solutions to the quadratic equation x² + 10x = 75, rounded to the nearest tenth, are x ≈ 5.

Step-by-step explanation:

The given quadratic equation is x² + 10x = 75.

To solve this equation, we need to rearrange it to get 0 on one side.
x²+ 10x - 75 = 0

We can use the quadratic formula to find the solutions.
The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 10, and c = -75.
Substituting these values into the quadratic formula, we get:
x = (-10 ± √(10² - 4(1)(-75))) / 2(1)

Simplifying further:
x = (-10 ± √(100 + 300)) / 2
x = (-10 ± √400) / 2
x = (-10 ± 20) / 2

The two solutions are:
x = (-10 + 20) / 2 = 5
x = (-10 - 20) / 2 = -15

Rounding these solutions to the nearest tenth, we have:
x ≈ 5 (rounded to the nearest tenth)