Question

Х^2-х-6=0. .....????? ​

Answer 1

Регение предоставлено в прикрепленном файле.

Answer 2

To solve the quadratic equation $x^2 - x - 6 = 0$, we can use the factoring method or the quadratic formula. I'll show you both methods:

1. Factoring method: The equation $x^2 - x - 6 = 0$ can be factored as $(x-3)(x+2) = 0$. To find the solutions for $x$, set each factor to zero and solve for $x$:

$x - 3 = 0 \Rightarrow x = 3$

$x + 2 = 0 \Rightarrow x = -2$

So, the solutions for the equation are $x = 3$ and $x = -2$.

2. Quadratic formula: The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where the quadratic equation is in the form $ax^2 + bx + c = 0$.

For the equation $x^2 - x - 6 = 0$, the coefficients are: $a = 1$, $b = -1$, and $c = -6$.

Substitute these values into the quadratic formula:

$x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \cdot 1 \cdot (-6)}}{2 \cdot 1}$

Simplifying further:

$x = \frac{1 \pm \sqrt{1 + 24}}{2}$

$x = \frac{1 \pm \sqrt{25}}{2}$

$x = \frac{1 \pm 5}{2}$

This gives us two solutions:

$x = \frac{1 + 5}{2} = \frac{6}{2} = 3$

$x = \frac{1 - 5}{2} = \frac{-4}{2} = -2$

So, as we obtained from the factoring method, the solutions for the equation are $x = 3$ and $x = -2$.