Final answer:
To solve the equation x² + 13x + 24 = 0 to the nearest tenth, we can use the quadratic formula. The solutions are approximately -2.2 and -10.3.
Step-by-step explanation:
To solve the equation x² + 13x + 24 = 0 to the nearest tenth, we can use the quadratic formula. For an equation of the form ax² + bx + c = 0, the solutions are given by:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values from the equation we have:
x = (-13 ± √(13² - 4(1)(24))) / (2)
Simplifying further, we get:
x ≈ (-13 ± √(169 - 96)) / 2
x ≈ (-13 ± √73) / 2
Using a calculator to find the square root of 73, we have:
x ≈ (-13 ± 8.54) / 2
We can simplify this further by evaluating the two possible solutions:
x₁ ≈ (-13 + 8.54) / 2 ≈ -2.23
x₂ ≈ (-13 - 8.54) / 2 ≈ -10.27
Therefore, the solutions to the equation x² + 13x + 24 = 0 to the nearest tenth are approximately -2.2 and -10.3.