Question

5(x-4)²-(x+5)²=4x²+5

Answer 1

По фото а дальше:
-50x+55=5
x=1

Answer 2

To solve the equation 5(x-4)² - (x+5)² = 4x² + 5, you can follow these steps:

1. Expand the squared terms on both sides of the equation.

5(x-4)² expands to 5(x² - 8x + 16). (x+5)² expands to x² + 10x + 25.

So the equation becomes:

5(x² - 8x + 16) - (x² + 10x + 25) = 4x² + 5

2. Distribute the constants in the parentheses on the left side of the equation.

5x² - 40x + 80 - (x² + 10x + 25) = 4x² + 5

3. Now, combine like terms on both sides of the equation.

5x² - 40x + 80 - x² - 10x - 25 = 4x² + 5

Combine x² terms: (5x² - x² - 4x²) = 0. Combine x terms: (-40x - 10x) = -50x. Combine constants: (80 - 25) = 55.

So the equation simplifies to:

-50x + 55 = 4x² + 5

4. Move all terms to one side to set the equation to zero:

-50x + 55 - 4x² - 5 = 0

Combine constants: 50 - 5 - 55 = -10.

Now, the equation becomes:

-4x² - 10 = 0

5. Divide the entire equation by -1 to make it easier to work with:

4x² + 10 = 0

6. Subtract 10 from both sides of the equation:

4x² = -10

7. Divide both sides by 4 to solve for x²:

x² = -10/4 x² = -5/2

8. Take the square root of both sides:

x = ±√(-5/2)

Since you cannot take the square root of a negative number in the real number system, there are no real solutions to this equation. The solutions would be complex numbers:

x = ±i√(5/2), where "i" represents the imaginary unit.