solve the equation by completing the square. Round to the nearest tenth. x^2+2x=8
To complete the square, we need to add and subtract the square of half the coefficient of x, which is (2/2)^2 = 1:
x^2 + 2x + 1 - 1 = 8
Now we can simplify:
(x+1)^2 - 1 = 8
Add 1 to both sides:
(x+1)^2 = 9
Take the square root of both sides:
x+1 = ±√9
x+1 = ±3
Subtract 1 from both sides:
x = -1±3
We get two solutions: x = 2 and x = -4
Rounding to the nearest tenth is not necessary since the solutions are integers. Therefore, the solutions are x = 2 and x = -4.
So the answer would be written like; x=2, -4 yes?
Yes, that's correct! The solutions are x = 2 and x = -4.
Thank you Bot.
You're welcome! Don't hesitate to ask if you have any more questions.
To solve the equation x^2 + 2x = 8 by completing the square, we will follow these steps:
Step 1: Move the constant term (in this case, 8) to the other side of the equation:
x^2 + 2x - 8 = 0
Step 2: Take half of the coefficient of x, squared. In this case, half of 2 is 1, and 1 squared is 1:
x^2 + 2x + 1 - 8 - 1 = 0
Step 3: Rewrite the equation by grouping the perfect square terms together and rearranging the remaining terms:
(x^2 + 2x + 1) - 9 = 0
Step 4: Rewrite the equation using the perfect square:
(x + 1)^2 - 9 = 0
Step 5: Simplify the equation:
(x + 1)^2 = 9
Step 6: Take the square root of both sides of the equation:
√((x + 1)^2) = ±√(9)
Step 7: Solve for x. Taking the square root gives two possible scenarios:
(x + 1) = ±3
For the positive square root:
x + 1 = 3
Solving for x:
x = 3 - 1
x = 2
For the negative square root:
x + 1 = -3
Solving for x:
x = -3 - 1
x = -4
Therefore, the solutions to the equation x^2 + 2x = 8, rounded to the nearest tenth, are x = 2 and x = -4.