Question

Решить уравнение: x(x-2)-(x+5)² = 35

Answer 1

X(x-2)-(x+5)²=35
x²-2x-x²-10x-25=35
-12x=60
x=60:(-12)
x=-5

Answer 2

To solve the quadratic equation $x(x-2)-(x+5)^2 = 35$, follow these steps:

Step 1: Expand the equation.

Step 2: Simplify the equation to get a quadratic equation in standard form (ax^2 + bx + c = 0).

Step 3: Solve the quadratic equation using factorization or the quadratic formula.

Let's go through the steps one by one:

Step 1: Expand the equation. $x(x-2)-(x+5)^2 = 35$

Expanding the square term $(x+5)^2$ gives us: $x(x-2) - (x^2 + 10x + 25) = 35$

Step 2: Simplify the equation. Now distribute the negative sign to the terms inside the parentheses: $x^2 - 2x - x^2 - 10x - 25 = 35$

Combine the like terms: $-12x - 25 = 35$

Step 3: Solve the equation. To isolate the term with x, move the constant term (-25) to the right side by adding 25 to both sides of the equation: $-12x = 35 + 25$ $-12x = 60$

Now, solve for x by dividing both sides by -12: $x = \frac{60}{-12}$ $x = -5$

Therefore, the solution to the equation is $x = -5$.