Question

(2x-1)(2x+9)(x+2)(x+4)+9=0

Answer 1

Відповідь:

(2x-1)(2x+9)(x+2)(x+4)+9=0

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

2x-1=-9

2х = -8

х = -4

2x+9=-9

2х = -18

х = -9

x+2 = - 9

х = -11

х+4=-9

х = -13

Answer 2

To solve the equation (2x-1)(2x+9)(x+2)(x+4) + 9 = 0, we can follow these steps:

Step 1: Expand the expression Step 2: Set the expression equal to 0 Step 3: Solve for x

Let's go through each step:

Step 1: Expand the expression To expand the given expression, you can use the FOIL method (First, Outer, Inner, Last) or the distributive property.

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

Using the distributive property, we'll multiply the first two factors and then the last two factors:

= (4x^2 + 18x - 2x - 9)(x^2 + 6x + 8) + 9

Combine like terms:

= (4x^2 + 16x - 9)(x^2 + 6x + 8) + 9

Now, use the distributive property again to multiply the two remaining factors:

= 4x^2 * x^2 + 4x^2 * 6x + 4x^2 * 8 + 16x * x^2 + 16x * 6x + 16x * 8 - 9 * x^2 - 9 * 6x - 9 * 8 + 9

= 4x^4 + 24x^3 + 32x^2 + 16x^3 + 96x^2 + 128x - 9x^2 - 54x - 72 + 9

Step 2: Set the expression equal to 0

Now, we have the following equation:

4x^4 + 16x^3 + 24x^2 - 54x + 9 = 0

Step 3: Solve for x

Unfortunately, the given equation is a quartic equation (4th degree), and solving quartic equations algebraically can be complex and not always straightforward. Depending on the coefficients of the equation, there might be no real roots, or there might be some real and complex roots.

To find the exact solutions, you can try various numerical methods or use a computer algebra system. Alternatively, you can use graphing techniques or approximation methods to find approximate solutions.

Keep in mind that this equation might not have simple and nice solutions, and it could involve irrational or complex roots.