Question

(3x-1)(3x+2)+(4x+5)²=10x+21

Answer 1

9х в квадрате +6х-3х-2+16х в квадрате +40х+25=10х+21
25х в квадрате +43х+23=10х+21

Answer 2

Let's solve the given equation step by step:

(3x-1)(3x+2) + (4x+5)² = 10x + 21

Step 1: Expand the expressions on the left side of the equation:

(3x-1)(3x+2) = 9x^2 + 6x - 3x - 2 = 9x^2 + 3x - 2

(4x+5)² = (4x+5)(4x+5) = 16x^2 + 20x + 20x + 25 = 16x^2 + 40x + 25

Step 2: Now, substitute the expanded expressions back into the equation:

(9x^2 + 3x - 2) + (16x^2 + 40x + 25) = 10x + 21

Step 3: Combine like terms on the left side of the equation:

9x^2 + 16x^2 + 3x + 40x - 2 + 25 = 10x + 21

Step 4: Simplify further:

25x^2 + 43x + 23 = 10x + 21

Step 5: Move all terms to one side to set the equation equal to zero:

25x^2 + 43x + 23 - 10x - 21 = 0

Step 6: Combine like terms again:

25x^2 + 33x + 2 = 0

Now we have a quadratic equation in the form of ax^2 + bx + c = 0. To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = 25, b = 33, and c = 2:

x = (-(33) ± √(33^2 - 4 * 25 * 2)) / 2 * 25

x = (-33 ± √(1089 - 200)) / 50

x = (-33 ± √889) / 50

Since the square root of 889 is not a nice whole number, we'll leave the answer in simplified radical form:

x = (-33 + √889) / 50 or x = (-33 - √889) / 50

So the solutions to the equation are approximately:

x ≈ 0.3 or x ≈ -1.48

Please note that these values are approximations since we kept the square root in simplified radical form.