Question

1)9x-x^2=0 2)7x+10x^2+2=0 3)4x^2-9=0 4)7x-2x^2=6 540x-25x^2=7 6)20x+4x^2+25=0 7)n^2+5n-84=0

Answer 1

Пиши, если что-то не понятно.

Answer 2

To solve each quadratic equation, let's set each equation to zero and then factor or use the quadratic formula to find the solutions.

1. $9x - x^2 = 0$: $x(9 - x) = 0$ So, $x = 0$ or $x = 9$.

2. $7x + 10x^2 + 2 = 0$: $2(1 + 5x)(1 - x) = 0$ So, $x = -\frac{1}{5}$ or $x = 1$.

3. $4x^2 - 9 = 0$: $(2x + 3)(2x - 3) = 0$ So, $x = -\frac{3}{2}$ or $x = \frac{3}{2}$.

4. $7x - 2x^2 = 6$: $-2x^2 + 7x - 6 = 0$ This can be factored as $(2x - 3)(x - 2) = 0$. So, $x = \frac{3}{2}$ or $x = 2$.

5. $540x - 25x^2 = 7$: $-25x^2 + 540x - 7 = 0$ This equation is not easily factorable, so we can use the quadratic formula. $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ Here, $a = -25$, $b = 540$, and $c = -7$. Plugging these values into the formula, you'll get the solutions for $x$.

6. $20x + 4x^2 + 25 = 0$: $4(x^2 + 5x + 6) = 0$ This can be factored as $4(x + 2)(x + 3) = 0$. So, $x = -2$ or $x = -3$.

7. $n^2 + 5n - 84 = 0$: $(n + 12)(n - 7) = 0$ So, $n = -12$ or $n = 7$.