Question

Give the values of A, B, and C needed to write the equation's general form.
(5 + x)(5 - x) = 7

1. A = 1; B = 0; C = -18
2. A= -1; B = 0; C = 25
3. A = 25; B = 0; C = -1

Answer 1

Given:

The equation is:

$(5+x)(5-x)=7$

To find:

The value of A, B and C for the equation's general form.

Solution:

We have,

$(5+x)(5-x)=7$

Using distribution property, we get

$(5)(5)+(5)(-x)+(x)(5)+(x)(-x)=7$

$25-5x+5x-x^2=7$

$25-x^2=7$

Taking all terms on one side, we get

$25-x^2-7=0$

$-x^2+18=0$

$-(x^2-18)=0$

$x^2-18=0$

On comparing this equation with the general form of a quadratic equation $Ax^2+Bx+C=0$, we get

$A=1$

$B=0$

$C=-18$

Therefore, the correct option is 1.