0.06x^2-4x=1406

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Solution for 0.06x^2-4x=1406 equation: 


Simplifying
0.06x2 + -4x = 1406

Reorder the terms:
-4x + 0.06x2 = 1406

Solving
-4x + 0.06x2 = 1406

Solving for variable 'x'.

Reorder the terms:
-1406 + -4x + 0.06x2 = 1406 + -1406

Combine like terms: 1406 + -1406 = 0
-1406 + -4x + 0.06x2 = 0

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

Divide each side by '0.06'.
-23433.33333 + -66.66666667x + x2 = 0

Move the constant term to the right:

Add '23433.33333' to each side of the equation.
-23433.33333 + -66.66666667x + 23433.33333 + x2 = 0 + 23433.33333

Reorder the terms:
-23433.33333 + 23433.33333 + -66.66666667x + x2 = 0 + 23433.33333

Combine like terms: -23433.33333 + 23433.33333 = 0.00000
0.00000 + -66.66666667x + x2 = 0 + 23433.33333
-66.66666667x + x2 = 0 + 23433.33333

Combine like terms: 0 + 23433.33333 = 23433.33333
-66.66666667x + x2 = 23433.33333

The x term is -66.66666667x.  Take half its coefficient (-33.33333334).
Square it (1111.111112) and add it to both sides.

Add '1111.111112' to each side of the equation.
-66.66666667x + 1111.111112 + x2 = 23433.33333 + 1111.111112

Reorder the terms:
1111.111112 + -66.66666667x + x2 = 23433.33333 + 1111.111112

Combine like terms: 23433.33333 + 1111.111112 = 24544.444442
1111.111112 + -66.66666667x + x2 = 24544.444442

Factor a perfect square on the left side:
(x + -33.33333334)(x + -33.33333334) = 24544.444442

Calculate the square root of the right side: 156.666666659

Break this problem into two subproblems by setting 
(x + -33.33333334) equal to 156.666666659 and -156.666666659.


Subproblem 1
x + -33.33333334 = 156.666666659

Simplifying
x + -33.33333334 = 156.666666659

Reorder the terms:
-33.33333334 + x = 156.666666659

Solving
-33.33333334 + x = 156.666666659

Solving for variable 'x'.

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

Add '33.33333334' to each side of the equation.
-33.33333334 + 33.33333334 + x = 156.666666659 + 33.33333334

Combine like terms: -33.33333334 + 33.33333334 = 0.00000000
0.00000000 + x = 156.666666659 + 33.33333334
x = 156.666666659 + 33.33333334

Combine like terms: 156.666666659 + 33.33333334 = 189.999999999
x = 189.999999999

Simplifying
x = 189.999999999


Subproblem 2
x + -33.33333334 = -156.666666659

Simplifying
x + -33.33333334 = -156.666666659

Reorder the terms:
-33.33333334 + x = -156.666666659

Solving
-33.33333334 + x = -156.666666659

Solving for variable 'x'.

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

Add '33.33333334' to each side of the equation.
-33.33333334 + 33.33333334 + x = -156.666666659 + 33.33333334

Combine like terms: -33.33333334 + 33.33333334 = 0.00000000
0.00000000 + x = -156.666666659 + 33.33333334
x = -156.666666659 + 33.33333334

Combine like terms: -156.666666659 + 33.33333334 = -123.333333319
x = -123.333333319

Simplifying
x = -123.333333319


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {189.999999999, -123.333333319}

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