solve the equation by completing the square. round to the nearest tenth. x^2+8x=10
A. 1.1, 9.1
B. 1.1, -9.1
C. -1.1, 9.1
D. -1.1,-9.1
my answer is A is that correct
I dont get it
x^2 + 8x + 16 = 10+16
(x+4)^2 = 26
x+4 = ±√26
x = -4 ±√26
Nope, not A
4,2
To solve the equation x^2 + 8x = 10 by completing the square, follow these steps:
1. Move the constant term to the other side:
x^2 + 8x - 10 = 0
2. Divide the coefficient of x by 2 and square it:
(8/2)^2 = 16
3. Add the result from step 2 to both sides of the equation:
x^2 + 8x + 16 - 10 = 16
x^2 + 8x + 6 = 16
4. Rewrite the left side of the equation as a perfect square trinomial:
(x + 4)^2 = 16
5. Take the square root of both sides (considering both positive and negative square roots):
x + 4 = ±√16
x + 4 = ±4
6. Solve for x:
x = -4 ± 4
So, the solutions to the equation x^2 + 8x = 10 are:
A. 1.1, 9.1
B. 1.1, -9.1
C. -1.1, 9.1
D. -1.1, -9.1
Now, let's check if your answer A is correct:
Plugging in the values of x (1.1 and 9.1) into the original equation, we get:
(1.1)^2 + 8(1.1) = 10
12.1 + 8.8 = 10
20.9 = 10
This shows that both values of x are not valid solutions. Therefore, your answer A is incorrect.
The correct answer is D. -1.1, -9.1.