Final answer:
The solutions to the equation rounded to the nearest tenth are approximately x = 8 + √21 and x = 8 - √21.
Step-by-step explanation:
To solve the equation x2-24x+70=-8x+27, we can start by rearranging it:
x2-24x+8x+70-27=0
x2-16x+43=0
Now we can use the quadratic formula, which is x = (-b ± √(b²-4ac))/(2a). In this equation, a = 1, b = -16, and c = 43. Substituting these values, we get:
x = (-(-16) ± √((-16)²-4(1)(43)))/(2(1))
x = (16 ± √(256-172))/2
x = (16 ± √84)/2
x = (16 ± 2√21)/2
x = 8 ± √21
Therefore, the solutions to the equation rounded to the nearest tenth are approximately x = 8 + √21 and x = 8 - √21.