Question

Корень -8x-5x+7=1-2x

Answer 1

Корень из - 8х? Или как или из вс ей левой части?

Answer 2

-8х-5х+7=1-2х 
-13х+7=1-2х
-13х+2х=1-7
-11х=-6
х=6/11(дробь)

Answer 3

To solve the equation $\sqrt{-8x-5x+7}=1-2x$, we need to follow these steps:

Step 1: Combine like terms on both sides of the equation. Step 2: Square both sides of the equation to eliminate the square root. Step 3: Solve the resulting quadratic equation. Step 4: Check for any extraneous solutions introduced during the process.

Let's go through these steps one by one:

Step 1: Combine like terms on both sides of the equation: $\sqrt{-13x + 7} = 1 - 2x$.

Step 2: Square both sides of the equation to eliminate the square root: $(\sqrt{-13x + 7})^2 = (1 - 2x)^2$.

Squaring the left side: $-13x + 7 = (1 - 2x)^2$.

Step 3: Expand and solve the quadratic equation on the right side: $-13x + 7 = 1 - 4x + 4x^2$.

Step 4: Rearrange the equation to set it to zero (standard form of a quadratic equation): $4x^2 - 4x - 6 = 0$.

Now we have a quadratic equation in the standard form $ax^2 + bx + c = 0$, where $a = 4$, $b = -4$, and $c = -6$. To solve this quadratic equation, we can use the quadratic formula:

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

Substitute the values of $a$, $b$, and $c$ into the formula:

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 \cdot 4 \cdot (-6)}}{2 \cdot 4}.$

$x = \frac{4 \pm \sqrt{16 + 96}}{8}.$

$x = \frac{4 \pm \sqrt{112}}{8}.$

$x = \frac{4 \pm 4\sqrt{7}}{8}.$

Now, we have two potential solutions:

$x_1 = \frac{4 + 4\sqrt{7}}{8} = \frac{1 + \sqrt{7}}{2},$

$x_2 = \frac{4 - 4\sqrt{7}}{8} = \frac{1 - \sqrt{7}}{2}.$

So, the two solutions to the equation are $x = \frac{1 + \sqrt{7}}{2}$ and $x = \frac{1 - \sqrt{7}}{2}$.