Question

1)-3х²+240х+2100=0 2)-0.25х²+37.5+900=0

Answer 1

:::::Объяснение:::::::::::

Answer 2

To solve these quadratic equations, you can use the quadratic formula, which is given by:

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

where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

Let's solve each equation separately:

1. $-3x^2 + 240x + 2100 = 0$

In this equation, a = -3, b = 240, and c = 2100. Now, plug these values into the quadratic formula:

$x = \frac{-240 \pm \sqrt{240^2 - 4(-3)(2100)}}{2(-3)}$

Now, calculate the discriminant (the value inside the square root):

$D = b^2 - 4ac = (240)^2 - 4(-3)(2100)$ $D = 57600 - (-25200)$ $D = 57600 + 25200$ $D = 82800$

Now, plug the discriminant back into the quadratic formula:

$x = \frac{-240 \pm \sqrt{82800}}{-6}$

Now, you can simplify and calculate the roots:

$x = \frac{-240 \pm \sqrt{82800}}{-6} \approx \frac{-240 \pm 288}{-6}$

Now, calculate the two possible solutions:

1st solution: $x_1 = \frac{-240 + 288}{-6} = \frac{48}{-6} = -8$

2nd solution: $x_2 = \frac{-240 - 288}{-6} = \frac{-528}{-6} = 88$

So, the solutions to the first equation are $x_1 = -8$ and $x_2 = 88$.

2. $-0.25x^2 + 37.5 + 900 = 0$

In this equation, a = -0.25, b = 0 (since there is no x-term), and c = 900. Now, plug these values into the quadratic formula:

$x = \frac{0 \pm \sqrt{0^2 - 4(-0.25)(900)}}{2(-0.25)}$

Now, calculate the discriminant:

$D = 0^2 - 4(-0.25)(900) = 0 - (-225) = 225$

Now, plug the discriminant back into the quadratic formula:

$x = \frac{0 \pm \sqrt{225}}{-0.5}$

Now, simplify and calculate the roots:

$x = \frac{0 \pm 15}{-0.5}$

Now, calculate the two possible solutions:

1st solution: $x_1 = \frac{0 + 15}{-0.5} = \frac{15}{-0.5} = -30$

2nd solution: $x_2 = \frac{0 - 15}{-0.5} = \frac{-15}{-0.5} = 30$

So, the solutions to the second equation are $x_1 = -30$ and $x_2 = 30$.