3x(7x-4)+6x-(13-24x^2)=

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Solution for 3x(7x-4)+6x-(13-24x^2)= equation:


Simplifying
3x(7x + -4) + 6x + -1(13 + -24x2) = 0

Reorder the terms:
3x(-4 + 7x) + 6x + -1(13 + -24x2) = 0
(-4 * 3x + 7x * 3x) + 6x + -1(13 + -24x2) = 0
(-12x + 21x2) + 6x + -1(13 + -24x2) = 0
-12x + 21x2 + 6x + (13 * -1 + -24x2 * -1) = 0
-12x + 21x2 + 6x + (-13 + 24x2) = 0

Reorder the terms:
-13 + -12x + 6x + 21x2 + 24x2 = 0

Combine like terms: -12x + 6x = -6x
-13 + -6x + 21x2 + 24x2 = 0

Combine like terms: 21x2 + 24x2 = 45x2
-13 + -6x + 45x2 = 0

Solving
-13 + -6x + 45x2 = 0

Solving for variable 'x'.

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

Divide each side by '45'.
-0.2888888889 + -0.1333333333x + x2 = 0

Move the constant term to the right:

Add '0.2888888889' to each side of the equation.
-0.2888888889 + -0.1333333333x + 0.2888888889 + x2 = 0 + 0.2888888889

Reorder the terms:
-0.2888888889 + 0.2888888889 + -0.1333333333x + x2 = 0 + 0.2888888889

Combine like terms: -0.2888888889 + 0.2888888889 = 0.0000000000
0.0000000000 + -0.1333333333x + x2 = 0 + 0.2888888889
-0.1333333333x + x2 = 0 + 0.2888888889

Combine like terms: 0 + 0.2888888889 = 0.2888888889
-0.1333333333x + x2 = 0.2888888889

The x term is -0.1333333333x.  Take half its coefficient (-0.06666666665).
Square it (0.004444444442) and add it to both sides.

Add '0.004444444442' to each side of the equation.
-0.1333333333x + 0.004444444442 + x2 = 0.2888888889 + 0.004444444442

Reorder the terms:
0.004444444442 + -0.1333333333x + x2 = 0.2888888889 + 0.004444444442

Combine like terms: 0.2888888889 + 0.004444444442 = 0.293333333342
0.004444444442 + -0.1333333333x + x2 = 0.293333333342

Factor a perfect square on the left side:
(x + -0.06666666665)(x + -0.06666666665) = 0.293333333342

Calculate the square root of the right side: 0.54160256

Break this problem into two subproblems by setting 
(x + -0.06666666665) equal to 0.54160256 and -0.54160256.

Subproblem 1

x + -0.06666666665 = 0.54160256 Simplifying x + -0.06666666665 = 0.54160256 Reorder the terms: -0.06666666665 + x = 0.54160256 Solving -0.06666666665 + x = 0.54160256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = 0.54160256 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = 0.54160256 + 0.06666666665 x = 0.54160256 + 0.06666666665 Combine like terms: 0.54160256 + 0.06666666665 = 0.60826922665 x = 0.60826922665 Simplifying x = 0.60826922665

Subproblem 2

x + -0.06666666665 = -0.54160256 Simplifying x + -0.06666666665 = -0.54160256 Reorder the terms: -0.06666666665 + x = -0.54160256 Solving -0.06666666665 + x = -0.54160256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + x = -0.54160256 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + x = -0.54160256 + 0.06666666665 x = -0.54160256 + 0.06666666665 Combine like terms: -0.54160256 + 0.06666666665 = -0.47493589335 x = -0.47493589335 Simplifying x = -0.47493589335

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.60826922665, -0.47493589335}

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