Question

3х(1+12х)+(6х-1)(6х+1)=2,5х

Answer 1

Ответ:

x1=$\frac{-1-\sqrt1153 }{288}$

x2=$\frac{-1+\sqrt1153}{288}$

Answer 2

To solve the equation 3x(1 + 12x) + (6x - 1)(6x + 1) = 2.5x, we'll begin by simplifying the equation and bringing all the terms to one side to obtain a quadratic equation. Then we can solve it by factoring or using the quadratic formula.

Let's simplify the equation step by step:

3x(1 + 12x) + (6x - 1)(6x + 1) = 2.5x

Expanding the expressions inside the parentheses:

3x + 36x^2 + 36x^2 + 6x - x - 1 = 2.5x

Combining like terms:

72x^2 + 8x - 1 = 2.5x

Moving all terms to one side:

72x^2 + 8x - 2.5x - 1 = 0

Simplifying further:

72x^2 + 5.5x - 1 = 0

Now we have a quadratic equation in the form ax^2 + bx + c = 0, where: a = 72 b = 5.5 c = -1

To solve the quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values, we get:

x = (-5.5 ± √((5.5)^2 - 4(72)(-1))) / (2(72))

Simplifying further:

x = (-5.5 ± √(30.25 + 288)) / 144

x = (-5.5 ± √(318.25)) / 144

x = (-5.5 ± 17.83) / 144

Now, we can solve for two possible values of x:

x1 = (-5.5 + 17.83) / 144

x1 = 12.33 / 144

x1 ≈ 0.0854

x2 = (-5.5 - 17.83) / 144

x2 = -23.33 / 144

x2 ≈ -0.1618

Therefore, the solutions to the equation 3x(1 + 12x) + (6x - 1)(6x + 1) = 2.5x are approximately x ≈ 0.0854 and x ≈ -0.1618.