Question

(4x+1)²-(1-3x)(1+3x)=(5x+2)²

Answer 1

Пошаговое объяснение:

Подобное решение на фото

Answer 2

Пошаговое объяснение:

(4x+1)²-(1-3x)(1+3x)=(5x+2)²

16х²+8х+1-(1²-9х²)=25х²+20х+4

16х²+8х+1-1+9х²=25х²+20х+4

16х²+8х+9х²-25х²-20х=4

-12х=4

х=4/(-12)

x=$-\frac{1}{3}$

Answer 3

To solve the equation (4x+1)² - (1-3x)(1+3x) = (5x+2)², we can first expand and simplify both sides of the equation and then solve for x. Here are the steps to do that:

1. Expand the expressions on both sides of the equation: (4x+1)² - (1-3x)(1+3x) = (5x+2)²

   (4x+1)(4x+1) - [(1)(1) - (1)(3x) + (-3x)(1) - (-3x)(3x)] = (5x+2)(5x+2)

2. Simplify the expressions further:

   (16x² + 8x + 1) - (1 - 3x + 3x - 9x²) = (25x² + 20x + 4)

3. Remove parentheses and combine like terms:

   16x² + 8x + 1 - 1 + 3x - 3x + 9x² = 25x² + 20x + 4

4. Combine like terms on both sides:

   25x² - 16x² + 9x² + 8x - 3x - 3x + 1 - 1 = 25x² + 20x + 4

   (25x² - 16x² + 9x²) + (8x - 3x - 3x) + (1 - 1) = 25x² + 20x + 4

   18x² + 2x = 25x² + 20x + 4

5. Move all terms to one side of the equation to set it equal to zero:

   18x² + 2x - 25x² - 20x - 4 = 0

6. Combine like terms:

   (-7x² - 18x - 4) = 0

7. Now, we have a quadratic equation in the form of ax² + bx + c = 0:

   -7x² - 18x - 4 = 0

8. To solve for x, we can use the quadratic formula:

   x = (-b ± √(b² - 4ac)) / (2a)

   In this case, a = -7, b = -18, and c = -4.

   x = (-(-18) ± √((-18)² - 4(-7)(-4))) / (2(-7))

9. Now, calculate the discriminant under the square root:

   Discriminant = (-18)² - 4(-7)(-4) = 324 - 112 = 212

10. Plug the discriminant back into the quadratic formula:

x = (18 ± √212) / (-14)

11. Finally, simplify further by dividing all terms by 2:

x = (9 ± √53) / (-7)

So, the solutions for the equation (4x+1)² - (1-3x)(1+3x) = (5x+2)² are:

x = (9 + √53) / (-7) and x = (9 - √53) / (-7)