Question

(4x + 5)² + (2 - 3x)² = (3 + 5)²

Answer 1

Решение на фото...................

Answer 2

The given equation is a quadratic equation. Let's solve it step by step:

Given equation: (4x + 5)² + (2 - 3x)² = (3 + 5)²

First, expand the squares:

(4x + 5)² = 16x² + 40x + 25 (2 - 3x)² = 4 - 12x + 9x² (3 + 5)² = 64

Substitute these expanded forms back into the original equation:

16x² + 40x + 25 + 4 - 12x + 9x² = 64

Combine like terms:

25x² + 28x + 29 = 64

Subtract 64 from both sides:

25x² + 28x - 35 = 0

Now you have a quadratic equation in standard form. To solve for x, you can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this equation, a = 25, b = 28, and c = -35.

Calculate the discriminant (b² - 4ac):

Discriminant = 28² - 4 * 25 * -35 = 784 + 3500 = 4284

Since the discriminant is positive, there are two real solutions for x:

x = (-28 + √4284) / 50 ≈ 0.548 x = (-28 - √4284) / 50 ≈ -1.348

So, the solutions for the given equation are approximately x = 0.548 and x = -1.348.