Question

X²-17x=-10x-3-x² Решите уравнение пожалуйста

Answer 1

X^2 - 17x = - 10x - 3  - x^2
x^2 + x^2 - 17x + 10x + 3 = 0 
2x^2 - 7x + 3 = 0 
D = 49 - 24 = 25
x1 = ( 7 + 5)/4 = 3;
x2 = ( 7 - 5)/4 = 0,5

Answer 2

Solving the Equation x² - 17x = -10x - 3 - x²

To solve the equation x² - 17x = -10x - 3 - x², we can simplify it by combining like terms and rearranging the equation. Let's go through the steps:

1. Combine like terms on both sides of the equation: - On the left side, we have x² - 17x. - On the right side, we have -10x - 3 - x². - Combining these terms, we get: x² - 17x = -11x - 3.

2. Move all terms to one side of the equation: - To do this, we can add 11x and 3 to both sides of the equation: x² - 17x + 11x + 3 = -11x - 3 + 11x + 3. - Simplifying this, we get: x² - 6x + 3 = 0.

3. Now, we have a quadratic equation in the form ax² + bx + c = 0, where a = 1, b = -6, and c = 3. We can solve this quadratic equation using various methods, such as factoring, completing the square, or using the quadratic formula.

Since the equation x² - 6x + 3 = 0 does not easily factor, let's solve it using the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / (2a).

Substituting the values of a, b, and c into the quadratic formula, we get: x = (-(-6) ± √((-6)² - 4(1)(3))) / (2(1)).

Simplifying this expression, we have: x = (6 ± √(36 - 12)) / 2, x = (6 ± √24) / 2, x = (6 ± 2√6) / 2.

Simplifying further, we get two possible solutions: x₁ = (6 + 2√6) / 2, x₂ = (6 - 2√6) / 2.

Simplifying the solutions, we have: x₁ = 3 + √6, x₂ = 3 - √6.

Therefore, the solutions to the equation x² - 17x = -10x - 3 - x² are: x₁ = 3 + √6, x₂ = 3 - √6.

Please let me know if you need any further clarification or assistance!