Question

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

Answer 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.