Question

(х-9)²=-х²+15х+50................

Answer 1

X^2-18x+81+x^2-15x-50=0
2x^2-32x+31
Решай квадратное уравнение, проучишь два корня, вот твой и ответ

Answer 2

Let's simplify the equation step by step:

1. Expand the left side of the equation using the square of a binomial:

(х - 9)² = х² - 18х + 81

The equation becomes:

х² - 18х + 81 = -х² + 15х + 50

2. Rearrange the terms to bring all the terms to one side of the equation:

х² + х² - 18х - 15х + 81 - 50 = 0

2х² - 33х + 31 = 0

Now we have a quadratic equation in standard form.

3. Solve the quadratic equation using factoring, completing the square, or the quadratic formula. In this case, the equation does not factor easily, so we'll use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Using the formula, we have:

x = (-(-33) ± √((-33)² - 4(2)(31))) / (2(2))

Simplifying further:

x = (33 ± √(1089 - 248)) / 4

x = (33 ± √841) / 4

x = (33 ± 29) / 4

Now we have two possible solutions:

x₁ = (33 + 29) / 4 = 62 / 4 = 15.5 x₂ = (33 - 29) / 4 = 4 / 4 = 1

Therefore, the solutions to the equation (х - 9)² = -х² + 15х + 50 are x₁ = 15.5 and x₂ = 1.