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
My answer is B.
B is correct
Well, solving equations can sometimes make us feel a bit square, but let's tackle this one together!
To complete the square, we'll first take half of the coefficient of x and square it. The coefficient of x is 8, so half of that is 4. Squaring 4 gives us 16.
Now, we'll add 16 to both sides of the equation to maintain balance. Our equation becomes x^2 + 8x + 16 = 26.
The left side of the equation can be factored as a perfect square: (x + 4)^2 = 26.
To isolate x, we take the square root of both sides, remembering to consider both the positive and negative roots: x + 4 = ±√26.
Finally, subtracting 4 from both sides gives us: x = -4 ± √26.
Rounding to the nearest tenth, the two solutions are approximately -1.1 and 9.1.
So, your answer is correct! Well done, you're smarter than a clown bot! The correct answer is A. 1.1, 9.1.
To solve the equation x^2 + 8x = 10 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 + 8x - 10 = 0
Step 2: Take half of the coefficient of x (which is 8) and square it:
(8/2)^2 = 4^2 = 16
Step 3: Add the result from step 2 to both sides of the equation:
x^2 + 8x + 16 - 10 = 16
x^2 + 8x + 6 = 16
Step 4: Rewrite the left side of the equation as a perfect square trinomial. To do this, take the coefficient of x, divide it by 2, square the result, and add it to both sides:
(x + 4)^2 = 16 + 6
(x + 4)^2 = 22
Step 5: Take the square root of both sides of the equation:
x + 4 = ±√22
Step 6: Solve for x by subtracting 4 from both sides:
x = -4 ± √22
Rounding to the nearest tenth, this yields two possible solutions:
x ≈ -4 + √22 ≈ 1.1
x ≈ -4 - √22 ≈ -9.1
Thus, the correct answer is B. 1.1, -9.1
To solve the equation by completing the square, follow these steps:
1. Begin with the equation: x^2 + 8x = 10
2. Move the constant term (10) to the right side of the equation:
x^2 + 8x - 10 = 0
3. Take half of the coefficient of x (in this case, 8) and square it:
(8/2)^2 = 16
4. Add the result from step 3 to both sides of the equation:
x^2 + 8x + 16 - 10 = 16
x^2 + 8x + 6 = 16
5. Write the left side of the equation as a perfect square trinomial:
(x + 4)^2 = 16
6. Take the square root of both sides of the equation:
√((x + 4)^2) = √16
x + 4 = ±4
7. Solve for x by subtracting 4 from both sides for each solution:
For x + 4 = 4: x = 4 - 4 = 0
For x + 4 = -4: x = -4 - 4 = -8
So, the solutions to the equation x^2 + 8x = 10 (rounded to the nearest tenth) are:
A. 1.1, 9.1 (incorrect)
B. 1.1, -9.1 (correct)
C. -1.1, 9.1 (incorrect)
D. -1.1, -9.1 (incorrect)
The correct answer is B. 1.1, -9.1.