Question

Решите уравнение (2-5х)^2=9 Помогите пожалуйста...

Answer 1

4-20х+25х²-9=0
25х²-20х-5=0
5х²-4х-1=0
D=b²-4ac
D=16+20=36
√D=36=6

x=4-6/5=-0,4
х=4+6/5=2

Answer 2

Solving the Equation (2-5x)^2 = 9

To solve the equation (2-5x)^2 = 9, we can follow these steps:

Step 1: Expand the square on the left side of the equation. Step 2: Set the resulting expression equal to 9. Step 3: Solve for x.

Let's go through each step in detail.

Step 1: Expand the square

To expand the square, we need to multiply (2-5x) by itself. This can be done using the distributive property:

(2-5x)^2 = (2-5x)(2-5x)

Expanding this expression, we get:

(2-5x)(2-5x) = 4 - 10x - 10x + 25x^2

Simplifying further, we have:

4 - 20x + 25x^2

Step 2: Set the expression equal to 9

Now that we have the expanded expression, we can set it equal to 9:

4 - 20x + 25x^2 = 9

Step 3: Solve for x

To solve for x, we need to rearrange the equation into a quadratic form (ax^2 + bx + c = 0). In this case, we have:

25x^2 - 20x + 4 = 9

Subtracting 9 from both sides, we get:

25x^2 - 20x - 5 = 0

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 25, b = -20, and c = -5. Substituting these values into the quadratic formula, we get:

x = (-(-20) ± √((-20)^2 - 4(25)(-5))) / (2(25))

Simplifying further, we have:

x = (20 ± √(400 + 500)) / 50

x = (20 ± √900) / 50

x = (20 ± 30) / 50

This gives us two possible solutions:

x1 = (20 + 30) / 50 = 50 / 50 = 1 x2 = (20 - 30) / 50 = -10 / 50 = -1/5

Therefore, the solutions to the equation (2-5x)^2 = 9 are x = 1 and x = -1/5.

Note: Please double-check the calculations as there might be a possibility of errors.