Solve the equation by completing the square. Round to the nearest tenth.
x squared plus 8 x equals 10
A. 1.1, 9.1
B. 1.1, -9.1
C.-1.1, 9.1
D. -1.1, -9.1
To solve by completing the square, we want to get the constant term on one side of the equation and the x terms on the other side. So we start with the equation:
x^2 + 8x = 10
We should move the constant to the other side to isolate the x terms:
x^2 + 8x - 10 = 0
Next, we complete the square for the x terms. To do this, we take half of the coefficient of x (which is 8) and square it:
(8/2)^2 = 16
Add and subtract this value inside the parentheses:
x^2 + 8x + 16 - 16 - 10 = 0
(x + 4)^2 - 26 = 0
Rearrange the equation:
(x + 4)^2 = 26
Now we take the square root of both sides to solve for x:
x + 4 = ±√26
x = -4 ± √26
Rounded to the nearest tenth, x is approximately equal to:
-4 + √26 ≈ -1.1
-4 - √26 ≈ -9.1
Therefore, the answer is D. -1.1, -9.1.