Question

(x²+x²)-5*(x²-x)-6=0​

Answer 1

Ответ:

Ответ детально в фото.

Объяснение:

Answer 2

To solve the quadratic equation $2x^2 - 5x^2 + 5x - 6 = 0$, first combine like terms to simplify the equation:

$2x^2 - 5x^2 + 5x - 6 = 0$

Now, add and subtract the $x^2$ terms:

$-3x^2 + 5x - 6 = 0$

Now, you have a quadratic equation in the form $ax^2 + bx + c = 0$, where $a = -3$, $b = 5$, and $c = -6$.

To solve this quadratic equation, you can use the quadratic formula:

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

In this case:

$a = -3$ $b = 5$ $c = -6$

Now, plug these values into the quadratic formula:

$x = \frac{-5 \pm \sqrt{5^2 - 4(-3)(-6)}}{2(-3)}$

Simplify:

$x = \frac{-5 \pm \sqrt{25 - 72}}{-6}$

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

$25 - 4(-3)(-6) = 25 - 72 = -47$

Since the discriminant is negative, the quadratic equation has no real solutions. However, it does have complex solutions. Let's continue to find those complex solutions:

$x = \frac{-5 \pm \sqrt{-47}}{-6}$

To deal with the square root of a negative number, we can express it in terms of the imaginary unit $i$:

$x = \frac{-5 \pm \sqrt{47}i}{-6}$

So, the solutions to the quadratic equation are:

$x_1 = \frac{-5 + \sqrt{47}i}{-6}$ $x_2 = \frac{-5 - \sqrt{47}i}{-6}$

These are the complex solutions to the equation $2x^2 - 5x^2 + 5x - 6 = 0$.