Question

Помогите решить квадратные уравнения!!!! 1) 2x в квадрате+2x=5 2) (2-x)(2x+1)=(2+x)(x-2) Пожалуйста, заранее спасибо!!!! Дам 200 баллов, если ответите четко и подробно и правильно!!!

Answer 1

1)2x²+2x=5
   2x²+2x-5=0, D=4+40=44,√D=2√11
  x1=(-4+2√11)/4=(-2+√11)/2

  x2=(-4-2√11)/4=(-2-√11)/2

2)(2-x)(2x+1)=(2+x)(x-2)
   4x+2-2x²-x=2x-4+x²-2x
   -2x²+3x+2=x²-4
   3x²-3x-6=0
   x²-x-2=0, D=1+8=9, √D=3
   x1=(1+3)/2=4/2=2
   x2=(1-3)/2=-2/2=-1

Answer 2

Solving the Quadratic Equations

Let's solve the given quadratic equations step by step.

Equation 1: 2x^2 + 2x = 5

To solve this equation, we can rearrange it to the standard quadratic form: ax^2 + bx + c = 0. In this case, a = 2, b = 2, and c = -5.

1. Start by subtracting 5 from both sides of the equation: 2x^2 + 2x - 5 = 0

2. Next, we can use the quadratic formula to find the solutions for x: x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values, we get: x = (-2 ± √(2^2 - 4 * 2 * -5)) / (2 * 2) x = (-2 ± √(4 + 40)) / 4 x = (-2 ± √44) / 4

Simplifying further: x = (-2 ± 2√11) / 4 x = -1/2 ± √11/2

Therefore, the solutions to the equation 2x^2 + 2x = 5 are: x = -1/2 + √11/2 and x = -1/2 - √11/2. Equation 2: (2-x)(2x+1) = (2+x)(x-2)

To solve this equation, we can expand both sides and simplify:

1. Expand the left side of the equation: (2 - x)(2x + 1) = 4x + 2 - 2x^2 - x

2. Expand the right side of the equation: (2 + x)(x - 2) = 2x - 4 + x^2 - 2x

3. Simplify both sides of the equation: 4x + 2 - 2x^2 - x = 2x - 4 + x^2 - 2x

4. Rearrange the equation to the standard quadratic form: -2x^2 - x + 4x + 2 - 2x - 2x + x^2 - 2x + 4 = 0

5. Combine like terms: -x^2 - 2x + 6 = 0

6. Solve the quadratic equation: x^2 + 2x - 6 = 0

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values, we get: x = (-2 ± √(2^2 - 4 * 1 * -6)) / (2 * 1) x = (-2 ± √(4 + 24)) / 2 x = (-2 ± √28) / 2

Simplifying further: x = (-2 ± 2√7) / 2 x = -1 ± √7

Therefore, the solutions to the equation (2-x)(2x+1) = (2+x)(x-2) are: x = -1 + √7 and x = -1 - √7. I hope this helps! Let me know if you have any further questions.