Question

Решить (x+2)(x-2)-x(x-6)=0

Answer 1

$(x-2)(x+2)-x(x-6)=x^{2} -4-x^{2} -6x=-6x-4$

Answer 2

To solve the equation $(x+2)(x-2) - x(x-6) = 0$, follow these steps:

Step 1: Expand the expressions on both sides of the equation.

Step 2: Simplify and collect like terms.

Step 3: Set the equation equal to zero.

Step 4: Factorize the equation.

Step 5: Find the values of $x$ that satisfy the equation.

Let's go through each step:

Step 1: Expand the expressions: $(x+2)(x-2) = x \cdot x + x \cdot (-2) + 2 \cdot x + 2 \cdot (-2) = x^2 - 2x + 2x - 4 = x^2 - 4$

$x(x-6) = x^2 - 6x$

Step 2: Simplify and collect like terms: Now, the equation becomes: $x^2 - 4 - x^2 + 6x = 0$

Step 3: Set the equation equal to zero: $x^2 - x^2 + 6x - 4 = 0$

Step 4: Factorize the equation: Since the $x^2$ terms cancel out, we are left with $6x - 4 = 0$.

Step 5: Find the values of $x$ that satisfy the equation: To find the value of $x$, solve for $x$ in the equation $6x - 4 = 0$.

$6x = 4$

$x = \frac{4}{6} = \frac{2}{3}$

So, the solution to the equation $(x+2)(x-2) - x(x-6) = 0$ is $x = \frac{2}{3}$.