Question

1000x+(444x-399x)-(685x+353x)x=7

Answer 1

Ответ:

$x_{1} =\frac{7}{1038},x_{2} = 1$

Пошаговое объяснение:

1000x+(45x)-1038x*x=7

1000x+45x-1038$x^{2}$=7

1045x-1038$x^{2}$=7

1045x-1038$x^{2}$-7=0

-1038$x^{2}$+1045x-7=0

x*(1038x-7)-(1038x-7)=0

(1038x-7)*(x-1)=0

1038x-7=0

x-1=0

Answer 2

Let's simplify the given expression step by step.

$1000x + (444x - 399x) - (685x + 353x)x = 7$

First, let's simplify the terms inside the parentheses:

$1000x + 45x - (1038x)x = 7$

Now, multiply the terms inside the parentheses:

$1000x + 45x - 1038x^2 = 7$

Next, move all terms to one side to set the equation to zero:

$1038x^2 - 1000x - 45x - 7 = 0$

Combine like terms:

$1038x^2 - 1045x - 7 = 0$

Now, the equation is in the form $ax^2 + bx + c = 0$, where $a = 1038$, $b = -1045$, and $c = -7$.

You can solve this quadratic equation using the quadratic formula:

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

Plugging in the values:

$x = \frac{1045 \pm \sqrt{(-1045)^2 - 4(1038)(-7)}}{2(1038)}$

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

$b^2 - 4ac = (-1045)^2 - 4(1038)(-7)$ $= 1092025 - 29016$ $= 1063009$

The discriminant is positive, so there are two real solutions for $x$. Now, plug in the values:

$x = \frac{1045 \pm \sqrt{1063009}}{2(1038)}$

$x = \frac{1045 \pm 1032}{2076}$

This gives two possible solutions for $x$:

1. $x = \frac{1045 + 1032}{2076} = \frac{2077}{2076} \approx 1.0005$

2. $x = \frac{1045 - 1032}{2076} = \frac{13}{2076} \approx 0.0063$

So, the solutions for the given equation are $x \approx 1.0005$ and $x \approx 0.0063$.