In ordinary mathematics, assuming that x = X and that X2 denotes x2 or x-squared, there cannot be a counterexample since the statement is TRUE.
However, there are two assumptions made that could be false and so could give rise to counterexamples.
1. x is not the same as X. If, for example X = 4x then X = -20 so that X2 = 400.
2a. X2 is not X2 but X times 2. In that case X2 = -10.
2b. X2 is x2 modulo 7, for example. Then X2 = 4.
Twenty-Five x2 + 10x = 8 x2 + 10x + 25 = 8 + 25 (x + 5)2 = 33
x2 = 6482 = 64x = 8
if x2 + 7 = 37, then x2 = 29 and x = ±√29
f(x) = x2 + 3 ----> f(5) = (5)2 + 3 ----> f(5) = 28
6x - 1 = 29 => 6x = 30 => x = 5 Then x2 + x = 25 + 5 = 30
x2 + 2y = 52 + 2*2 = 25 + 4 = 29
x2 + 10x = 0 x2 + 10x + 25 = 25 (x + 5)2 = 25 x + 5 = +-5 x1 = 0 x2 =10
x2 - 6x = 16 ∴ x2 - 6x + 9 = 25 ∴ (x - 3)2 = 25 ∴ x - 3 = 25 ∴ x = 28
If: x2+16 = 25 Then: x = 3
x^2 + y^2 = r^2
x1:y1 = x2:y2 4:-2 = x2:5 x2 = (4*5)/-2 x2 = -10
x2+4x+4 = 25 x2+4x+4-25 = 0 x2+4x-21 = 0 (x+7)(x-3) = 0 x = -7 or x = 3
5. A circle with centre (0,0) has equation: x2 + y2 = radius2 With: x2 + y2 = 25 = 52 The radius is 5.
x2 - 10x + 25 = 0(x - 5)(x - 5) = 0x - 5 = 0x = 5
We can't calculate what it equals until we know the value of ' x '.
9
x = +5 or x = -5