contestada

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

Respuesta :

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

[tex]2x^2-5x-7=0[/tex]

Step-by-step explanation:

Given the equation:

[tex]x+9=2(x-1)^2[/tex]

Using identity:

[tex](a-b)^2=a^2-2ab+b^2[/tex]

then;

[tex]x+9 = 2(x^2-2x+1)[/tex]

Using distributive property: [tex]a \cdot (b+c) = a\cdot b+ a\cdot c[/tex]

[tex]x+9 = 2x^2-4x+2[/tex]

Subtract x from both sides we have;

[tex]9= 2x^2-5x+2[/tex]

Subtract 9 from both sides we have;

[tex]0=2x^2-5x-7[/tex]

or

[tex]2x^2-5x-7=0[/tex]

Therefore, the equation [tex]2x^2-5x-7=0[/tex] is written in the form of [tex]ax^2+bx+c=0[/tex]