3x^2-1x-30=30

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Solution for 3x^2-1x-30=30 equation:


Simplifying
3x2 + -1x + -30 = 30

Reorder the terms:
-30 + -1x + 3x2 = 30

Solving
-30 + -1x + 3x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + -30 + -1x + 3x2 = 30 + -30

Combine like terms: -30 + -30 = -60
-60 + -1x + 3x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-60 + -1x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-20 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -0.3333333333x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -0.3333333333x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -0.3333333333x + x2 = 0 + 20
-0.3333333333x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-0.3333333333x + x2 = 20

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 20 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 20 + 0.02777777779

Combine like terms: 20 + 0.02777777779 = 20.02777777779
0.02777777779 + -0.3333333333x + x2 = 20.02777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 20.02777777779

Calculate the square root of the right side: 4.475240527

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 4.475240527 and -4.475240527.

Subproblem 1

x + -0.1666666667 = 4.475240527 Simplifying x + -0.1666666667 = 4.475240527 Reorder the terms: -0.1666666667 + x = 4.475240527 Solving -0.1666666667 + x = 4.475240527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 4.475240527 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 4.475240527 + 0.1666666667 x = 4.475240527 + 0.1666666667 Combine like terms: 4.475240527 + 0.1666666667 = 4.6419071937 x = 4.6419071937 Simplifying x = 4.6419071937

Subproblem 2

x + -0.1666666667 = -4.475240527 Simplifying x + -0.1666666667 = -4.475240527 Reorder the terms: -0.1666666667 + x = -4.475240527 Solving -0.1666666667 + x = -4.475240527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -4.475240527 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -4.475240527 + 0.1666666667 x = -4.475240527 + 0.1666666667 Combine like terms: -4.475240527 + 0.1666666667 = -4.3085738603 x = -4.3085738603 Simplifying x = -4.3085738603

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.6419071937, -4.3085738603}

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