4X^2+6X-2=(X-1)^2 Найти корни уравнения

Question

4X^2+6X-2=(X-1)^2

Найти корни уравнения

Answer 1

4x^2+6x-2=(x-1)^2

(6x-2)-(x-1)^2+4x^2=0

(6x-2)+(4x^2-x^2+2x-1)=0

(6x-2)+(3x^2+2x-1)=0

2(3x-1)+(x+1)(3x-1)=0

(x+3)(3x-1)=0

1) x+3=0 => x=-3

2) 3x-1=0 => x=1/3

Answer 2

4X^2+6X-2=(X-1)^2

 4X^2+6X-2=X^2-2x+1

 3x2 + 8x - 3 = 0
D = b2 - 4ac
D = 64 + 36 = 100 = 10^2

x1,2 = -b ± √D/2a
x1 = -8 + 10/6 = 2/6 = 1/3
x2 = -8 - 10/6 = - 18/6 = -3
Ответ: x1 = 1/3 ; x2 = -3