could you please double check my work
question:find the roots of the equation 2x^2+8x=12 by completing the square. leave answer in simplest radical form.
work and answer: c=(b/2)^2
c(4/2)^2=4
2x^2 +8x=12
divide everything by 2
x^2 + 4x=6
x^2+4x+4=10
(x+2)(x+2)
square root of (X+2)^2= square root of 10
x+2= square root of 10
subtract 2 from each side
and my answer was x= -2 plus or minus the square root of 10
right on.
To double-check your work for finding the roots of the equation 2x^2 + 8x = 12 by completing the square, let's go through the steps again.
Step 1: Divide everything by 2
2x^2 + 8x = 12
Divide by 2: x^2 + 4x = 6
Step 2: Add the square of half of the coefficient of x to both sides
In this case, the coefficient of x is 4, so half of it is 2. We want to add (2^2) = 4 to both sides:
x^2 + 4x + 4 = 6 + 4
Simplifying further, we get:
x^2 + 4x + 4 = 10
Step 3: Rewrite the left side as a perfect square
The left side can be expressed as (x + 2)^2:
(x + 2)^2 = 10
Step 4: Take the square root of both sides
Taking the square root of both sides, we get:
√((x + 2)^2) = √10
Step 5: Solve for x
Now we can solve for x by taking both the positive and negative square roots of 10:
x + 2 = ± √10
Finally, subtract 2 from both sides:
x = -2 ± √10
Your answer, x = -2 ± √10, is correct. Well done!