Question

5(x-10)-(x-20)(x-10)-10x=0

Answer 1

Х(2)-х во второй степени
5х-50-(х(2)-10х-20х+200)-10х=0
5х-50-х(2)+10х+20х-200-10х=0
5х-х(2)+10х+20х-10х=0+50-200
25х-х(2)=-150
х-х(2)=-150:(-25)
х-х(2)=6

Answer 2

Let's solve the given equation step by step:

5(x - 10) - (x - 20)(x - 10) - 10x = 0

Step 1: Expand the expressions within parentheses.

5x - 50 - (x^2 - 10x - 20x + 200) - 10x = 0

Step 2: Combine like terms.

5x - 50 - (x^2 - 30x + 200) - 10x = 0

Step 3: Distribute the negative sign to the terms inside the second set of parentheses.

5x - 50 - x^2 + 30x - 200 - 10x = 0

Step 4: Combine like terms again.

5x - x^2 + 20x - 250 = 0

Step 5: Move all terms to one side of the equation to set it to zero.

-x^2 + 25x - 250 = 0

Step 6: Multiply the entire equation by -1 to make the leading coefficient positive.

x^2 - 25x + 250 = 0

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -25, and c = 250.

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

x = (-b ± √(b^2 - 4ac)) / 2a

Substitute the values of a, b, and c:

x = (25 ± √((-25)^2 - 4 * 1 * 250)) / 2 * 1

x = (25 ± √(625 - 1000)) / 2

x = (25 ± √(-375)) / 2

The value inside the square root is negative, which means the quadratic equation has no real solutions. It has complex solutions. Let's proceed:

x = (25 ± √(375)i) / 2

So, the solutions for the given equation are:

x = (25 + √375i) / 2 x = (25 - √375i) / 2

Both solutions involve the imaginary unit "i" because the discriminant (b^2 - 4ac) was negative.