Question

Решите уравнение (6x-1)(x+1)-4(9x+2)=-1 ПОДРОБНО

Answer 1

Решение на прикреплённом фото

Answer 2

Solving the Equation: (6x-1)(x+1)-4(9x+2)=-1

To solve the equation (6x-1)(x+1)-4(9x+2)=-1, 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

To expand the equation, we will multiply the terms using the distributive property.

Expanding the equation (6x-1)(x+1)-4(9x+2)=-1 gives us:

(6x)(x) + (6x)(1) + (-1)(x) + (-1)(1) - (4)(9x) - (4)(2) = -1

Simplifying further, we have:

6x^2 + 6x - x - 1 - 36x - 8 = -1

Step 2: Simplify the equation

Now, let's simplify the equation by combining like terms.

Combining like terms, we get:

6x^2 + (6x - x - 36x) - 1 - 8 = -1

Simplifying further, we have:

6x^2 - 31x - 9 = -1

Step 3: Solve for x

To solve for x, we will set the equation equal to zero and use factoring or the quadratic formula.

Setting the equation equal to zero, we have:

6x^2 - 31x - 9 + 1 = 0

Simplifying further, we get:

6x^2 - 31x - 8 = 0

Now, we can either factor the quadratic equation or use the quadratic formula to solve for x.

Using the quadratic formula, which 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)

For our equation, a = 6, b = -31, and c = -8.

Using the quadratic formula, we have:

x = (-(-31) ± √((-31)^2 - 4(6)(-8))) / (2(6))

Simplifying further, we get:

x = (31 ± √(961 + 192)) / 12

x = (31 ± √1153) / 12

Therefore, the solutions for the equation (6x-1)(x+1)-4(9x+2)=-1 are:

x = (31 + √1153) / 12 and x = (31 - √1153) / 12.

Please note that the exact values of x depend on the value of √1153, which is an irrational number.

I hope this helps! Let me know if you have any further questions.