x2 + 49 = x2 - (-49) = x2 - (-1)(49) = x2 - (i2)(72) = x2 - (7i)2 = (x - 7i)(x + 7i) where i is the imaginary square root of -1.
-x2 + x + 42 = -[x2 - x - 42] = -[x2 - 7x + 6x - 42] = -[x*(x - 7) + 6*(x - 7)] = -(x - 7)*(x + 6)
x2 + 2x -6 = 0 x2 + 2x + 1 = 7 (x + 1)2 = 7 x = -1 ± √7
y=x2-12x+7
Since there are only terms in x2 and constants, but none in x, completing the square is not an option! x2 - 14 = 7 x2 = 21 and so x2 = sqrt(21)
x4 + x2 - 42 Let x2 = t, so that x4 = t2 t2 + t - 42 since -42 = 7(-6) and 7 + (-6) = 1, then t2 + t - 42 = (t - 6)(t + 7) = (x2 - 6)(x2 + 7) By replacing t with x2. So we have, x4 + x2 - 42 = (x2 - 6)(x2 + 7) = [x2 - (square root of 6)2](x2 + 7) = (x - sq. root of 6 )(x + sq. root of 6)(x2 + 7)
if x2 + 7 = 37, then x2 = 29 and x = ±√29
x2-49 = (x-7)(x+7)
x2 + 49 = x2 - (-49) = x2 - (-1)(49) = x2 - (i2)(72) = x2 - (7i)2 = (x - 7i)(x + 7i) where i is the imaginary square root of -1.
x2+6x-7 = (x+7)(x-1) when factored
-x2 + x + 42 = -[x2 - x - 42] = -[x2 - 7x + 6x - 42] = -[x*(x - 7) + 6*(x - 7)] = -(x - 7)*(x + 6)
x2 - 14x + 49(x - 7) (x - 7)
x2 + 2x -6 = 0 x2 + 2x + 1 = 7 (x + 1)2 = 7 x = -1 ± √7
-7
If the variables are x1 & x2 the solution is : 1) x1=x1+x2; 2) x2=x1-x2; 3) x1=x1-x2; EX: x1=1 , x2=6; 1) x1= 1+6 = 7 2) x2= 7-6 =1 3 x1=7-1 =6 ============================================
x2+2x-63 = (x-7)(x+9) when factored
y=x2-12x+7