Answer:
the solution to the equation (4x + 2)2 = 2x2 + 16x + 4 is x = 0
Explanation:
When we expand the left-hand side of the equation (4x + 2)2, we get:
(4x + 2)2 = (4x + 2)(4x + 2) = 16x2 + 8x + 8x + 4 = 16x2 + 16x + 4
So the equation becomes:
16x2 + 16x + 4 = 2x2 + 16x + 4
Next, we can subtract 2x2 + 16x + 4 from both sides:
16x2 + 16x + 4 - (2x2 + 16x + 4) = 0
After simplifying, we get:
16x2 + 16x + 4 - 2x2 - 16x - 4 = 0
Combine like terms:
(16x2 - 2x2) + (16x - 16x) + (4 - 4) = 0
14x2 + 0 + 0 = 0
Simplifying:
14x2 = 0
Finally, we divide both sides by 14:
14x2/14 = 0/14
x2 = 0
Taking the square root of both sides:
√x2 = √0
x = 0
So the solution to the equation (4x + 2)2 = 2x2 + 16x + 4 is x = 0.