Question

X^(2)-7x+c=(x+a)^(2)

Answer 1

This equation is a difference of squares factorization. It states that the difference between the square of x and 7x plus some constant c is equal to the square of (x+a). To solve for a and c, we can expand both sides of the equation:

X^(2) - 7x + c = x^(2) + 2ax + a^(2)

And we can set them equal to each other and solve for a and c:

x^(2) - 7x + c = x^(2) + 2ax + a^(2)

-2ax - a^(2) = -7x + c

a = (7x - c) / 2x

c = x^(2) - 7x + a^(2)

Note that this is valid as long as x is not equal to 0.