Solve the equation x, squared, minus, 8, x, minus, 43, equals, minus, 21x 2 −8x−43=−21 to the nearest tenth.

The given equation is x^2 - 8x - 43 = -21.

First, we need to simplify the equation. We can do this by adding 21 to both sides of the equation to get rid of the negative sign on the right side. This gives us:

x^2 - 8x - 43 + 21 = 0

Simplify further to get:

x^2 - 8x - 22 = 0

Next, we need to solve this quadratic equation. We can do this by using the quadratic formula, which is:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

In our equation, a = 1, b = -8, and c = -22.

Substitute these values into the quadratic formula to get:

x = [8 ± sqrt((-8)^2 - 41(-22))] / 2*1 x = [8 ± sqrt(64 + 88)] / 2 x = [8 ± sqrt(152)] / 2 x = [8 ± 12.3] / 2

This gives us two possible solutions:

x = (8 + 12.3) / 2 = 10.15 x = (8 - 12.3) / 2 = -2.15

So, the solutions to the equation x^2 - 8x - 43 = -21 are x = 10.15 and x = -2.15, to the nearest tenth.