Question

5/6x1/12x+1/2x=3 3/4

Answer 1

Ответ:

Надеюсь все понятно написал

Answer 2

To solve the equation $\frac{5}{6}x \cdot \frac{1}{12}x + \frac{1}{2}x = \frac{3}{4}$, follow these steps:

Step 1: Simplify the left side of the equation.

• $\frac{5}{6}x \cdot \frac{1}{12}x = \frac{5}{72}x^2$

So, the equation becomes:

$\frac{5}{72}x^2 + \frac{1}{2}x = \frac{3}{4}$

Step 2: Multiply both sides of the equation by 72 to eliminate fractions:

$72 \left(\frac{5}{72}x^2 + \frac{1}{2}x\right) = 72 \cdot \frac{3}{4}$

This simplifies to:

$5x^2 + 36x = 54$

Step 3: Move all terms to one side of the equation to set it to zero:

$5x^2 + 36x - 54 = 0$

Step 4: To solve this quadratic equation, you can use the quadratic formula:

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

In this case, $a = 5$, $b = 36$, and $c = -54$. Plug these values into the quadratic formula:

$x = \frac{-36 \pm \sqrt{36^2 - 4 \cdot 5 \cdot (-54)}}{2 \cdot 5}$

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

$\text{Discriminant} = 36^2 - 4 \cdot 5 \cdot (-54)$

$\text{Discriminant} = 1296 + 1080$

$\text{Discriminant} = 2376$

Now, plug the discriminant back into the quadratic formula:

$x = \frac{-36 \pm \sqrt{2376}}{10}$

Step 5: Simplify the square root:

$x = \frac{-36 \pm \sqrt{4 \cdot 594}}{10}$

$x = \frac{-36 \pm \sqrt{4 \cdot 9 \cdot 66}}{10}$

$x = \frac{-36 \pm 2 \sqrt{9 \cdot 66}}{10}$

$x = \frac{-36 \pm 2 \cdot 3 \sqrt{66}}{10}$

Now, you can further simplify this expression:

$x = \frac{-6 \pm 3 \sqrt{66}}{5}$

So, there are two possible solutions:

1. $x = \frac{-6 + 3 \sqrt{66}}{5}$
2. $x = \frac{-6 - 3 \sqrt{66}}{5}$

These are the solutions to the equation $\frac{5}{6}x \cdot \frac{1/12}x + \frac{1}{2}x = \frac{3}{4}$