Задание 16, стр 54

1.

$6x^2+5x-1=0$
$6x^2+6x-x-1=0$
$6x(x+1)-(x+1)=0$
$(6x-1)(x+1)=0$
$6x-1=0x+1=0$
$6x=1x=-1$
$x=\frac{1}{6}$

2.

$4x^2-8x+3=0$
$4x^2-2x-6x+3=0$
$2x(2x-1)-3(2x-1)=0$
$(2x-3)(2x-1)=0$
$2x-3=02x-1=0$
$2x=32x=1$
$x=\frac{3}{2}=1.5x=\frac{1}{2}=0.5$

3.

$2x^2-7x+5=0$
$2x^2-2x-5x+5=0$
$2x(x-1)-5(x-1)=0$
$(2x-5)(x-1)=0$
$2x-5=0x-1=0$
$2x=5x=1$.
$x=\frac{5}{2}=2.5$.

4.

$4x^2-8x+3=0$
$4x^2-6x-2x+3=0$
$\left(4x^2-2x\right)-(6x-3)=0$
$2x(2x-1)-3(2x-1)=0$
$(2x-3)\cdot (2x-1)=0$
$2x-3=02x-1=0$
$\begin{array}{cc}2x=3\hfill & 2x=1\hfill \\ x=\frac{3}{2}\hfill & x=\frac{1}{2}\hfill \end{array}$

5.

$4x^2-7x-11=0$
$4x^2-11x+4x-11=0$
$\left(4x^2+4x\right)-(11x+11)=0$
$4x(x+1)-11(x+1)=0$
$(x+1)\cdot (4x+11)=0$
$x=14x=11$
$x=\frac{11}{4}$

6.

$3x^2-13x-30=0$.
$3x^2-18x+5x-30=0$
$\left(3x^2-18x\right)+(5x-30)=0$
$3x(x-6)+5(x-6)=0$
$(3x+5)(x-6)=0$
$3x+5=0x=6$
$3x=-5$
$x=-\frac{5}{3}$

7.

$4x^2+8x+3=0$
$4x^2+6x+2x+3=0$
$\left(4x^2+2x\right)+(6x+3)=0$
$2x(2x+1)+3(2x+1)=0$
$(2x+3)\cdot (2x+1)=0$
$2x=-32x=-1$
$x=-\frac{3}{2}x=-\frac{1}{2}$

8.

$2x^2+5x-3=0$
$2x^2+6x-x-3=0$
$\left(2x^2+6x\right)-(x+3)=0$
$2x(x+3)-1(x+3)=0$
$(2x-1)(x+3)=0$.
$2x=1x=-3$
$x=\frac{1}{2}$

9.

$3x^2-11x+8=0$
$3x^2-8x-3x+8=0$
$\left(3x^2-3x\right)-(8x-8)=0$
$3x(x-1)-8(x-1)=0$
$(3x-8)(x-1)=0$
$3x=8x=1$
$x=\frac{8}{3}$

© Posted with Ayla Ḧuseynova’s help. Acknowledgements to her!