6x^2+40x-25=0

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Solution for 6x^2+40x-25=0 equation: 


Simplifying
6x2 + 40x + -25 = 0

Reorder the terms:
-25 + 40x + 6x2 = 0

Solving
-25 + 40x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-4.166666667 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 6.666666667x + 4.166666667 + x2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 6.666666667x + x2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 6.666666667x + x2 = 0 + 4.166666667
6.666666667x + x2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
6.666666667x + x2 = 4.166666667

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 = 4.166666667 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 4.166666667 + 11.11111112

Combine like terms: 4.166666667 + 11.11111112 = 15.277777787
11.11111112 + 6.666666667x + x2 = 15.277777787

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 15.277777787

Calculate the square root of the right side: 3.908679801

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 3.908679801 and -3.908679801.


Subproblem 1
x + 3.333333334 = 3.908679801

Simplifying
x + 3.333333334 = 3.908679801

Reorder the terms:
3.333333334 + x = 3.908679801

Solving
3.333333334 + x = 3.908679801

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 = 3.908679801 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 3.908679801 + -3.333333334
x = 3.908679801 + -3.333333334

Combine like terms: 3.908679801 + -3.333333334 = 0.575346467
x = 0.575346467

Simplifying
x = 0.575346467


Subproblem 2
x + 3.333333334 = -3.908679801

Simplifying
x + 3.333333334 = -3.908679801

Reorder the terms:
3.333333334 + x = -3.908679801

Solving
3.333333334 + x = -3.908679801

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 = -3.908679801 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -3.908679801 + -3.333333334
x = -3.908679801 + -3.333333334

Combine like terms: -3.908679801 + -3.333333334 = -7.242013135
x = -7.242013135

Simplifying
x = -7.242013135


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.575346467, -7.242013135}

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