Question

Which shows the equation below written in the form ax2 + bx + c = 0?

x + 9 = 2(x - 1)2

A. 2x2 - 5x - 7 = 0
B. 2x2 - 3x + 11 = 0
C. 2x2 - 3x - 7 = 0
D. 2x2 - 5x + 11 = 0

Answer 1

Option A is correct

`2x^2-5x-7=0`

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`

Answer 2

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