Question

8x(1+12x)-(4x-3)(4x-3)=2x

Answer 1

8x(1+12x)-(4x-3)(4x-3)=2x
8x+96x^2-16x^2-12x-12x+9=2x
-16x+80x^2+9=2x
-16x+80x^2-2x-9=0
-18x+80x^2-9=0
80x^2-18x-9=0
Это уже квадратичное уравнение. Могу решить в комментарии если нужно

Answer 2

Let's simplify and solve the given equation step by step:

First, we can expand the second term on the left-hand side using the FOIL method:

8x(1+12x) - (4x-3)(4x-3) = 2x 8x + 96x^2 - (16x^2 - 24x - 24x + 9) = 2x (distributing the negative sign and simplifying) 8x + 96x^2 - (16x^2 - 48x + 9) = 2x (combining like terms) 8x + 96x^2 - 16x^2 + 48x - 9 = 2x (distributing the negative sign again)

Next, we can simplify the expression by combining like terms:

80x^2 + 56x - 9 = 0 (combining like terms)

Now we have a quadratic equation in standard form, where a=80, b=56, and c=-9. We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the values of a, b, and c, we get:

x = (-56 ± sqrt(56^2 - 4(80)(-9))) / 2(80) x = (-56 ± sqrt(3136 + 2880)) / 160 x = (-56 ± sqrt(6016)) / 160 x = (-56 ± 2sqrt(376)) / 160 x = (-7 ± sqrt(94)) / 20

Therefore, the solutions to the equation are:

x = (-7 + sqrt(94)) / 20 or x = (-7 - sqrt(94)) / 20