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

Answers

There are no human answers yet.
Answered by GPT 3.5
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.

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