Question

Решите уравнение (5x+4)^2-2(5x+4)-3=0

Answer 1

(5x+4)^2-2(5x+4)-3=0
25х^2+40х+16-10х-8-3=0
25х^2+30х+5=0/:5
5х^2+6х+1=0
х1=-5/5=-1
х2=-1/5=-0,2

Answer 2

Максимально подробное решение

Answer 3

To solve the quadratic equation $(5x+4)^2 - 2(5x+4) - 3 = 0$, we can use the substitution method to simplify the equation. Let $y = 5x + 4$. Now, we have the equation:

$y^2 - 2y - 3 = 0$

This is now a simple quadratic equation in terms of $y$, which we can solve using factoring, completing the square, or the quadratic formula. In this case, factoring is the easiest method:

$y^2 - 2y - 3 = 0$

$(y - 3)(y + 1) = 0$

Now, set each factor to zero and solve for $y$:

$y - 3 = 0$ or $y + 1 = 0$

$y = 3$ or $y = -1$

But remember that $y = 5x + 4$, so we can substitute back the original variable:

$5x + 4 = 3$ or $5x + 4 = -1$

Now, solve for $x$ in each case:

Case 1:

$5x + 4 = 3$

$5x = 3 - 4$

$5x = -1$

$x = \frac{-1}{5}$

Case 2:

$5x + 4 = -1$

$5x = -1 - 4$

$5x = -5$

$x = \frac{-5}{5}$

$x = -1$

So, the solutions to the equation are $x = \frac{-1}{5}$ and $x = -1$.