Question

4х^2-19х+32=-6x^2-6x+41

Answer 1

4х² - 19х  + 32 = - 6х² - 6х + 41
4х²  - 19х  + 32  + 6х²  + 6х  - 41 = 0
(4 + 6)х²  + (-19 +6)х  + (32 - 41) = 0
10х²  - 13х - 9  = 0
D = (-13)²  - 4*10 *(-9) =  169 +360 = 529 = 23²
D> 0  -  два корня уравнения
х₁ = ( - (-13)  - 23)/(2*10) = (13 - 23)/20 = -10/20 = -0,5
х₂ = ( -(-13) + 23)/(2*10) = (13 +23)/20  = 36/20 = 18/10 = 1,8

Answer 2

To solve the given equation, we need to combine like terms and bring all terms to one side to obtain a quadratic equation in standard form. Let's begin:

4x^2 - 19x + 32 = -6x^2 - 6x + 41

Rearranging the terms:

4x^2 + 6x^2 - 19x + 6x + 32 - 41 = 0

Combining like terms:

10x^2 - 13x - 9 = 0

Now we have a quadratic equation in standard form. To solve it, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our equation, a = 10, b = -13, and c = -9. Plugging these values into the quadratic formula, we get:

x = (-(-13) ± √((-13)^2 - 4 * 10 * (-9))) / (2 * 10)

Simplifying further:

x = (13 ± √(169 + 360)) / 20

x = (13 ± √529) / 20

x = (13 ± 23) / 20

We have two possible solutions:

x₁ = (13 + 23) / 20 = 36 / 20 = 9 / 5 = 1.8

x₂ = (13 - 23) / 20 = -10 / 20 = -1 / 2 = -0.5

Therefore, the solutions to the equation 4x^2 - 19x + 32 = -6x^2 - 6x + 41 are x = 1.8 and x = -0.5.