To solve this equation, we can start by expanding both sides of the equation:
Left side:(2x+1)² - 3(x-5)²= (2x+1)(2x+1) -3(x-5)(x-5)= 4x² + 2x + 2x + 1 - 3(x² - 10x + 25)= 4x² + 4x + 1 - 3x² + 30x - 75= x² + 34x - 74
Right side:(x+3)(x-3)= x² - 3x + 3x - 9= x² - 9
Now we can compare the two sides:
x² + 34x - 74 = x² - 9
Subtract x² from both sides:
34x - 74 = -9
Add 74 to both sides:
34x = 65
Divide by 34:
x = 65/34
Therefore, the solution to the equation is x = 65/34.
To solve this equation, we can start by expanding both sides of the equation:
Left side:
(2x+1)² - 3(x-5)²
= (2x+1)(2x+1) -3(x-5)(x-5)
= 4x² + 2x + 2x + 1 - 3(x² - 10x + 25)
= 4x² + 4x + 1 - 3x² + 30x - 75
= x² + 34x - 74
Right side:
(x+3)(x-3)
= x² - 3x + 3x - 9
= x² - 9
Now we can compare the two sides:
x² + 34x - 74 = x² - 9
Subtract x² from both sides:
34x - 74 = -9
Add 74 to both sides:
34x = 65
Divide by 34:
x = 65/34
Therefore, the solution to the equation is x = 65/34.