if (x + 3)(x -2) = 1
show that x^2 + x -7 = 0
Multiply out the (x + 3)(x -2), giving you
x^2 +x -6 = 1 ,
and then subtract 1 from both sides of that equation. You will get you the equation that you want to prove.
That proves it is true
thanks
To show that x^2 + x - 7 = 0, we need to expand the given equation and simplify it to match the desired equation.
Let's expand (x + 3)(x - 2):
(x + 3)(x - 2) = x(x) + x(-2) + 3(x) + 3(-2)
= x^2 - 2x + 3x - 6
= x^2 + x - 6
Now we need to manipulate the equation x^2 + x - 6 = 0 to match x^2 + x - 7 = 0. To do this, we need to add 1 to each side of the equation:
x^2 + x - 6 + 1 = 0 + 1
x^2 + x - 5 = 1
Now, to obtain x^2 + x - 7 = 0, we subtract 6 from each side of the equation:
(x^2 + x - 5) - 6 = 1 - 6
x^2 + x - 11 = -5
Finally, we add 4 to each side of the equation to obtain the desired equation:
(x^2 + x - 11) + 4 = -5 + 4
x^2 + x - 7 = -1
Hence, we have shown that (x + 3)(x - 2) = 1 implies x^2 + x - 7 = 0.