Question

2) 5x(x – 4) = (x – 8)²– 65;​

Answer 1

5x(x – 4) = (x – 8)²– 65

5х²-20х=х²-16х+64-65

5х²-20х-х²+16х+1=0

4х²-4х+1=0

(2х-1)²=0

2х-1=0

2х=1

х=½ или х=0,5

Answer 2

To solve the given equation $5x(x - 4) = (x - 8)^2 - 65$, follow these steps:

1. Expand the equation:

   $5x(x - 4) = (x - 8)^2 - 65$

   $5x^2 - 20x = x^2 - 16x + 64 - 65$

   Simplify the right side:

   $5x^2 - 20x = x^2 - 16x - 1$

2. Move all terms to one side to set the equation to zero:

   $5x^2 - x^2 - 20x + 16x - 1 = 0$

   Simplify:

   $4x^2 - 4x - 1 = 0$

3. Use the quadratic formula to solve for $x$:

   The quadratic formula states that for an equation in the form $ax^2 + bx + c = 0$, the solutions for $x$ are given by:

   $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

   In this case, $a = 4$, $b = -4$, and $c = -1$. Plug these values into the quadratic formula:

   $x = \frac{4 \pm \sqrt{(-4)^2 - 4(4)(-1)}}{2(4)}$

   $x = \frac{4 \pm \sqrt{48}}{8}$

   $x = \frac{4 \pm 4\sqrt{3}}{8}$

4. Simplify the solutions:

   The solutions for $x$ are:

   $x_1 = \frac{1 + \sqrt{3}}{2}$

   $x_2 = \frac{1 - \sqrt{3}}{2}$