6x^2-40x+30=07

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Solution for 6x^2-40x+30=07 equation: 


Simplifying
6x2 + -40x + 30 = 7

Reorder the terms:
30 + -40x + 6x2 = 7

Solving
30 + -40x + 6x2 = 7

Solving for variable 'x'.

Reorder the terms:
30 + -7 + -40x + 6x2 = 7 + -7

Combine like terms: 30 + -7 = 23
23 + -40x + 6x2 = 7 + -7

Combine like terms: 7 + -7 = 0
23 + -40x + 6x2 = 0

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

Divide each side by '6'.
3.833333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-3.833333333' to each side of the equation.
3.833333333 + -6.666666667x + -3.833333333 + x2 = 0 + -3.833333333

Reorder the terms:
3.833333333 + -3.833333333 + -6.666666667x + x2 = 0 + -3.833333333

Combine like terms: 3.833333333 + -3.833333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -3.833333333
-6.666666667x + x2 = 0 + -3.833333333

Combine like terms: 0 + -3.833333333 = -3.833333333
-6.666666667x + x2 = -3.833333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -3.833333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -3.833333333 + 11.11111112

Combine like terms: -3.833333333 + 11.11111112 = 7.277777787
11.11111112 + -6.666666667x + x2 = 7.277777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 7.277777787

Calculate the square root of the right side: 2.697735678

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 2.697735678 and -2.697735678.


Subproblem 1
x + -3.333333334 = 2.697735678

Simplifying
x + -3.333333334 = 2.697735678

Reorder the terms:
-3.333333334 + x = 2.697735678

Solving
-3.333333334 + x = 2.697735678

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 2.697735678 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 2.697735678 + 3.333333334
x = 2.697735678 + 3.333333334

Combine like terms: 2.697735678 + 3.333333334 = 6.031069012
x = 6.031069012

Simplifying
x = 6.031069012


Subproblem 2
x + -3.333333334 = -2.697735678

Simplifying
x + -3.333333334 = -2.697735678

Reorder the terms:
-3.333333334 + x = -2.697735678

Solving
-3.333333334 + x = -2.697735678

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -2.697735678 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -2.697735678 + 3.333333334
x = -2.697735678 + 3.333333334

Combine like terms: -2.697735678 + 3.333333334 = 0.635597656
x = 0.635597656

Simplifying
x = 0.635597656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.031069012, 0.635597656}

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