Question

X² + 3 |x+2|+ 4x +4 =

Answer 1

Пошаговое объяснение:

x^2+3(x+2)+4x+4=0, x+2≥0

x^2+3*(-(x+2))+4x+4=0, x+2<0

Система:

{x=-2; x=-5, x≥-2

{x=-2; x=1, x<-2

x=-2

x∈∅

Ответ:

x=-2

Answer 2

It looks like you have an equation with absolute value. To solve this equation, you'll need to consider two cases: one where the expression inside the absolute value is positive and one where it's negative. Let's break it down:

Given equation: $x^2 + 3 |x+2| + 4x + 4 = 0$

Case 1: $x+2$ is non-negative (i.e., $x+2 \geq 0$) In this case, you can remove the absolute value, and the equation becomes:

$x^2 + 3 (x+2) + 4x + 4 = 0$

Now, simplify and solve for $x$:

$x^2 + 3x + 6 + 4x + 4 = 0$

$x^2 + 7x + 10 = 0$

This is a quadratic equation, and you can use the quadratic formula to solve for $x$:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = 1$, $b = 7$, and $c = 10$. Plugging these values into the quadratic formula:

$x = \frac{-7 \pm \sqrt{7^2 - 4(1)(10)}}{2(1)}$

Now, calculate the discriminant ($b^2 - 4ac$):

$7^2 - 4(1)(10) = 49 - 40 = 9$

So the discriminant is positive. This means there are two real solutions:

$x_1 = \frac{-7 + \sqrt{9}}{2} = \frac{-7 + 3}{2} = -2$

$x_2 = \frac{-7 - \sqrt{9}}{2} = \frac{-7 - 3}{2} = -5$

Case 2: $x+2$ is negative (i.e., $x+2 < 0$) In this case, you can remove the absolute value and negate the expression inside the absolute value, making it positive:

$x^2 + 3 (-x-2) + 4x + 4 = 0$

Now, simplify and solve for $x$:

$x^2 - 3x - 6 + 4x + 4 = 0$

Combine like terms:

$x^2 + x - 2 = 0$

This is another quadratic equation. Use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

In this case, $a = 1$, $b = 1$, and $c = -2$. Plugging these values into the quadratic formula:

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

Calculate the discriminant:

$1^2 - 4(1)(-2) = 1 + 8 = 9$

Again, the discriminant is positive, so there are two real solutions:

$x_3 = \frac{-1 + \sqrt{9}}{2} = \frac{-1 + 3}{2} = 1$

$x_4 = \frac{-1 - \sqrt{9}}{2} = \frac{-1 - 3}{2} = -2$