Question

Решите уравнение (х+4)^2=2(4х+11)срочно!!!помогите,пожалуйста

Answer 1

(x+4)^2=2*(4x+11)
x^2+2*4*x+4^2=2*4x+2*11
x^2+8x+16=8x+22
x^2+8x-8x=22-16
x^2=6
x=корень из 6

Answer 2

Solving the Equation (x + 4)^2 = 2(4x + 11)

To solve the equation (x + 4)^2 = 2(4x + 11), we will follow these steps:

Step 1: Expand the equation Step 2: Simplify the equation Step 3: Solve for x

Let's go through each step in detail.

Step 1: Expand the equation

Expanding the equation (x + 4)^2 gives us x^2 + 8x + 16.

So, the equation becomes x^2 + 8x + 16 = 2(4x + 11).

Step 2: Simplify the equation

Now, let's simplify the equation by distributing the 2 on the right side:

x^2 + 8x + 16 = 8x + 22.

Next, let's move all the terms to one side of the equation:

x^2 + 8x - 8x + 16 - 22 = 0.

Simplifying further, we get:

x^2 - 6 = 0.

Step 3: Solve for x

To solve the equation x^2 - 6 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a).

In this case, a = 1, b = 0, and c = -6.

Plugging in the values, we get:

x = (0 ± √(0^2 - 4(1)(-6))) / (2(1)).

Simplifying further, we have:

x = ± √(24) / 2.

x = ± 2√6 / 2.

Simplifying the expression, we get:

x = ± √6.

Therefore, the solutions to the equation (x + 4)^2 = 2(4x + 11) are x = √6 and x = -√6.

Note: Please double-check the calculations to ensure accuracy.

Let me know if there's anything else I can help you with!