Question

9x^2+8=18x 2x=-x^2-1 20x+25x^2=-4

Answer 1

Ответ:

$\frac{2}{3}, \quad 1\frac{1}{3}; \quad -1; \quad -0,4;$

Объяснение:

$9x^{2}+8=18x;$

$9x^{2}-18x+8=0;$

$D=b^{2}-4ac;$

$D=(-18)^{2}-4 \cdot 9 \cdot 8=324-288=36;$

$x_{1,2}=\frac{-b \pm \sqrt{D}}{2a};$

$x_{1}=\frac{-(-18)+\sqrt{36}}{2 \cdot 9}=\frac{18+6}{18}=\frac{18}{18}+\frac{6}{18}=1+\frac{1}{3}=1\frac{1}{3};$

$x_{2}=\frac{-(-18)-\sqrt{36}}{2 \cdot 9}=\frac{18-6}{18}=\frac{18}{18}-\frac{6}{18}=1-\frac{1}{3}=\frac{2}{3};$

$2x=-x^{2}-1;$

$x^{2}+2x+1=0;$

$(x+1)^{2}=0;$

$x_{1}=x_{2}=-1;$

$20x+25x^{2}=-4;$

$25x^{2}+20x+4=0;$

$(5x+2)^{2}=0;$

$x_{1}=x_{2}=-\frac{2}{5}=-0,4;$

Answer 2

To solve each of these quadratic equations, we'll follow these steps:

1. Rewrite the equation in standard quadratic form: $ax^2 + bx + c = 0$.
2. Apply the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
3. Simplify and find the solutions.

Let's solve each equation one by one:

1. $9x^2 + 8 = 18x$:

First, move all terms to one side to get it in standard form: $9x^2 - 18x + 8 = 0$

Now, we can use the quadratic formula:

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

In this case, $a = 9$, $b = -18$, and $c = 8$.

$x = \frac{18 \pm \sqrt{(-18)^2 - 4 \cdot 9 \cdot 8}}{2 \cdot 9}$

$x = \frac{18 \pm \sqrt{324 - 288}}{18}$

$x = \frac{18 \pm \sqrt{36}}{18}$

Now, simplify further:

$x = \frac{18 \pm 6}{18}$

You have two solutions:

1. $x = \frac{18 + 6}{18} = \frac{24}{18} = \frac{4}{3}$
2. $x = \frac{18 - 6}{18} = \frac{12}{18} = \frac{2}{3}$

So, the solutions are $x = \frac{4}{3}$ and $x = \frac{2}{3}$.

2. $2x = -x^2 - 1$:

Rearrange the terms to get it in standard form:

$x^2 + 2x + 1 = 0$

Now, we can use the quadratic formula:

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

In this case, $a = 1$, $b = 2$, and $c = 1$.

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

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

$x = \frac{-2 \pm \sqrt{0}}{2}$

Since the discriminant ($b^2 - 4ac$) is zero, there is only one solution:

$x = \frac{-2}{2} = -1$

So, the solution is $x = -1$.

3. $20x + 25x^2 = -4$:

Rearrange the terms to get it in standard form:

$25x^2 + 20x + 4 = 0$