Question

(5х-1)² -(4х+3)²=9х²-25

Answer 1

Объяснение:

Решение уравнения на фото

Answer 2

Let's solve the given equation step by step:

Given equation: (5x - 1)² - (4x + 3)² = 9x² - 25

Step 1: Expand the squares on both sides of the equation: (5x - 1)² = (5x - 1) * (5x - 1) = 25x² - 10x + 1 (4x + 3)² = (4x + 3) * (4x + 3) = 16x² + 24x + 9

Step 2: Substitute the expanded expressions back into the original equation: (25x² - 10x + 1) - (16x² + 24x + 9) = 9x² - 25

Step 3: Combine like terms on both sides of the equation: 25x² - 10x + 1 - 16x² - 24x - 9 = 9x² - 25

Step 4: Simplify the equation further: (25x² - 16x²) + (-10x - 24x) + (1 - 9) = 9x² - 25

Step 5: Combine the terms: 9x² - 34x - 8 = 9x² - 25

Step 6: Now, we want to isolate the variable on one side. Subtract 9x² from both sides of the equation: 9x² - 9x² - 34x - 8 = 9x² - 9x² - 25

Step 7: Simplify the equation further: -34x - 8 = -25

Step 8: Now, isolate the variable x by moving the constant term to the other side. Add 8 to both sides: -34x - 8 + 8 = -25 + 8

Step 9: Simplify the equation further: -34x = -17

Step 10: Finally, solve for x by dividing both sides by -34: x = -17 / -34

Step 11: Simplify the fraction: x = 1/2

So, the solution to the equation is x = 1/2.