Question

X - 2x^2 = -17 решите уравнение

Answer 1

$2 {x}^{2} - x - 17 = 0 \\ D = 1 - 4 \times 2 \times ( - 17) = \\ = 1 + 136 = 137 \\ x_{1} = \frac{1 - \sqrt{137} }{4} \\ x_{2} = \frac{1 + \sqrt{137} }{4}$

Answer 2

To solve the equation X - 2x^2 = -17, we need to find the values of x that satisfy the equation.

Step 1: Put the equation in standard form (ax^2 + bx + c = 0): 2x^2 + X = 17

Step 2: Rearrange the equation: 2x^2 + X + 17 = 0

Now, we have a quadratic equation in the standard form: ax^2 + bx + c = 0, where: a = 2 b = 1 c = 17

Step 3: Use the quadratic formula to find the solutions for x: The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a

Substitute the values of a, b, and c into the formula: x = (-(1) ± √(1^2 - 4 * 2 * 17)) / (2 * 2)

x = (-1 ± √(1 - 136)) / 4 x = (-1 ± √(-135)) / 4

Step 4: Simplify the square root: Since the square root of a negative number is imaginary, we have complex solutions:

x = (-1 + √135i) / 4 x = (-1 - √135i) / 4

So, the solutions to the equation are: x = (-1 + √135i) / 4 x = (-1 - √135i) / 4