Question

9(2х+3)^2-25=0 решите пожалуйста с объяснениями

Answer 1

$9(2x+3)^2-25=0 \\ 9(2x+3)^2=25 \\ (2x+3)^2= \frac{25}{9} \\ 2x+3= \frac{5}{3} ; \ \ \ \ \ \ 2x+3= -\frac{5}{3} \\2x= \frac{5}{3}-3;\ \ \ \ \ \ 2x= -\frac{5}{3}-3; \\ 2x= \frac{5-3*3}{3};\ \ \ \ \ 2x= \frac{-5-3*3}{3} \\ 2x=- \frac{4}{3};\ \ \ \ \ \ \ \ 2x=- \frac{14}{3} \\ x_1=- \frac{2}{3};\ \ \ \ \ \ \ \ x_2= - \frac{7}{3}$

Answer 2

Solving the Equation 9(2x+3)^2-25=0

To solve the equation 9(2x+3)^2-25=0, we can follow these steps:

1. Isolate the squared term: - Add 25 to both sides of the equation to move the constant to the right side: 9(2x+3)^2 = 25.

2. Divide by 9: - Divide both sides by 9 to isolate the squared term: (2x+3)^2 = 25/9.

3. Take the square root: - Take the square root of both sides to solve for (2x+3): 2x+3 = ±√(25/9).

4. Solve for x: - Solve for x by subtracting 3 from both sides and then dividing by 2: x = (-3 ± √(25/9))/2.

Let's calculate the values of x using these steps.

Calculation

1. Isolate the squared term: - 9(2x+3)^2 = 25

2. Divide by 9: - (2x+3)^2 = 25/9

3. Take the square root: - 2x+3 = ±√(25/9) - 2x+3 = ±(5/3)

4. Solve for x: - 2x = -3 ± (5/3) - 2x = -3 + (5/3) or 2x = -3 - (5/3) - x = (-3 + 5/3)/2 or x = (-3 - 5/3)/2 - x = (2/3)/2 or x = (-14/3)/2 - x = 1/3 or x = -7/3

So, the solutions for the equation 9(2x+3)^2-25=0 are x = 1/3 and x = -7/3.

Conclusion

The solutions for the given equation are x = 1/3 and x = -7/3.