30x+2x*6x=3

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Solution for 30x+2x*6x=3 equation:


Simplifying
30x + 2x * 6x = 3

Reorder the terms for easier multiplication:
30x + 2 * 6x * x = 3

Multiply 2 * 6
30x + 12x * x = 3

Multiply x * x
30x + 12x2 = 3

Solving
30x + 12x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 30x + 12x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 30x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 10x + 4x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1 + 10x + 4x2)' equal to zero and attempt to solve:

Simplifying
-1 + 10x + 4x2 = 0

Solving
-1 + 10x + 4x2 = 0

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

Divide each side by '4'.
-0.25 + 2.5x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 2.5x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 2.5x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 2.5x + x2 = 0 + 0.25
2.5x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
2.5x + x2 = 0.25

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 0.25 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 0.25 + 1.5625

Combine like terms: 0.25 + 1.5625 = 1.8125
1.5625 + 2.5x + x2 = 1.8125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.346291202 and -1.346291202.


Subproblem 1
x + 1.25 = 1.346291202

Simplifying
x + 1.25 = 1.346291202

Reorder the terms:
1.25 + x = 1.346291202

Solving
1.25 + x = 1.346291202

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.346291202 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.346291202 + -1.25
x = 1.346291202 + -1.25

Combine like terms: 1.346291202 + -1.25 = 0.096291202
x = 0.096291202

Simplifying
x = 0.096291202


Subproblem 2
x + 1.25 = -1.346291202

Simplifying
x + 1.25 = -1.346291202

Reorder the terms:
1.25 + x = -1.346291202

Solving
1.25 + x = -1.346291202

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.346291202 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.346291202 + -1.25
x = -1.346291202 + -1.25

Combine like terms: -1.346291202 + -1.25 = -2.596291202
x = -2.596291202

Simplifying
x = -2.596291202


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.096291202, -2.596291202}
Solution
x = {0.096291202, -2.596291202}

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