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Verified Answer :

HomertheGenius

x + 9 = 2 ( x - 1 )²
x + 9 = 2 ( x² - 2 x + 1 )
x + 9 = 2 x² - 4 x + 2
- 2 x² + 4 x + x - 2 + 9 = 0
- 2 x² + 5 x + 7 = 0   / * ( -1 )
Answer:
A ) 2 x² - 5 x - 7 

Answer:

Option A is correct

\(2x^2-5x-7=0\)

Step-by-step explanation:

Given the equation:

\(x+9=2(x-1)^2\)

Using identity:

\((a-b)^2=a^2-2ab+b^2\)

then;

\(x+9 = 2(x^2-2x+1)\)

Using distributive property: \(a \cdot (b+c) = a\cdot b+ a\cdot c\)

\(x+9 = 2x^2-4x+2\)

Subtract x from both sides we have;

\(9= 2x^2-5x+2\)

Subtract 9 from both sides we have;

\(0=2x^2-5x-7\)

or

\(2x^2-5x-7=0\)

Therefore, the equation \(2x^2-5x-7=0\) is written in the form of \(ax^2+bx+c=0\)

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