Question

(х+3) в квадрате =2(х+3)+8

Answer 1

Ответ:

x²+6x+9=2x+6+8

x²+4x+1=0

D=16-4=12

x1=(-4+√12)/2=-2+√3

x2=(-4-√12)/2=-2-√3

Answer 2

To solve the equation $(x+3)^2 = 2(x+3) + 8$, we'll first expand the left-hand side and then simplify the equation step by step:

Expanding the left-hand side: $(x+3)^2 = (x+3)(x+3) = x^2 + 6x + 9$

Now, the equation becomes: $x^2 + 6x + 9 = 2(x+3) + 8$

Next, distribute the 2 on the right side of the equation: $x^2 + 6x + 9 = 2x + 6 + 8$

Combine like terms: $x^2 + 6x + 9 = 2x + 14$

Subtract $2x + 14$ from both sides to bring all terms to the left side: $x^2 + 6x + 9 - (2x + 14) = 0$

Now, simplify: $x^2 + 6x + 9 - 2x - 14 = 0$

Combine like terms again: $x^2 + 4x - 5 = 0$

Now, we have a quadratic equation. To solve it, we can use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In our equation, $a = 1$, $b = 4$, and $c = -5$. Plugging these values into the formula:

$x = \frac{-4 \pm \sqrt{4^2 - 4(1)(-5)}}{2(1)}$

$x = \frac{-4 \pm \sqrt{16 + 20}}{2}$

$x = \frac{-4 \pm \sqrt{36}}{2}$

$x = \frac{-4 \pm 6}{2}$

Now, we have two possible solutions for $x$:

1. $x = \frac{-4 + 6}{2} = \frac{2}{2} = 1$
2. $x = \frac{-4 - 6}{2} = \frac{-10}{2} = -5$

So, the equation $(x+3)^2 = 2(x+3) + 8$ has two solutions: $x = 1$ and $x = -5$.