Please solve: -5*(6x^3 - 4x^2 + x-3) = 0 and -(-x-9) -4 [3x-2(6+x) +5] = 0

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

You are only allowed to ask one question at a time, your question has been changed accordingly.

To solve -5*(6x^3 - 4x^2 + x-3) = 0

-5*(6x^3 - 4x^2 + x-3) = 0

=> 6x^3 - 4x^2 + x-3 = 0

=> 6x^3 - 6x^2 + 2x^2 - 2x + 3x  - 3 = 0

=> 6x^2(x = 1) + 2x(x - 1) + 3(x - 1) = 0

=> (x - 1)[6x^2 + 2x + 3] = 0

x1 =1

6x^2 + 2x + 3 = 0 gives us

x2 = -2/12 + sqrt(4 - 72)/12

=> -1/6 + i*sqrt 68 / 12

=> -1/6 + 2*i*sqrt 17 / 12

=> (-1 + i*sqrt 17)/6

x3 = (-1 -i*sqrt 17)/6

The solutions of the equation are: (1, (-1 + i*sqrt 17)/6, (-1 -i*sqrt 17)/6)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Supposing that you want to solve the equation in x, for no. 2, you'll have to re-write such as the expression provided to represent an equation:

-(-x-9) -4 [3x-2(6+x) +5] = 0

We'll solve what is inside round brackets:

x + 9 - 4*(3x - 12 - 2x + 5) = 0

We'll combine like terms inside brackets:

x + 9 - 4*(x - 7) = 0

We'll multiply by 4:

x + 9 - 4x + 28 = 0

We'll combine like terms:

-3x + 37 = 0

We'll isolate -3x to the left side:

-3x = -37

x = -37/-3

x = 37/3

The solution of the equation -(-x-9) -4 [3x-2(6+x) +5] = 0 is x = 37/3.

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