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. (4x + 2)2 = 2x2 + 16x + 4

User Ashareef
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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.

User Evan Jones
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