6x^2+9x-25=0

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Solution for 6x^2+9x-25=0 equation: 


Simplifying
6x2 + 9x + -25 = 0

Reorder the terms:
-25 + 9x + 6x2 = 0

Solving
-25 + 9x + 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 + 1.5x + x2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 1.5x + 4.166666667 + x2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 1.5x + x2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 1.5x + x2 = 0 + 4.166666667
1.5x + x2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
1.5x + x2 = 4.166666667

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 4.166666667 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 4.166666667 + 0.5625

Combine like terms: 4.166666667 + 0.5625 = 4.729166667
0.5625 + 1.5x + x2 = 4.729166667

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 4.729166667

Calculate the square root of the right side: 2.174664725

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.174664725 and -2.174664725.


Subproblem 1
x + 0.75 = 2.174664725

Simplifying
x + 0.75 = 2.174664725

Reorder the terms:
0.75 + x = 2.174664725

Solving
0.75 + x = 2.174664725

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.174664725 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.174664725 + -0.75
x = 2.174664725 + -0.75

Combine like terms: 2.174664725 + -0.75 = 1.424664725
x = 1.424664725

Simplifying
x = 1.424664725


Subproblem 2
x + 0.75 = -2.174664725

Simplifying
x + 0.75 = -2.174664725

Reorder the terms:
0.75 + x = -2.174664725

Solving
0.75 + x = -2.174664725

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.174664725 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.174664725 + -0.75
x = -2.174664725 + -0.75

Combine like terms: -2.174664725 + -0.75 = -2.924664725
x = -2.924664725

Simplifying
x = -2.924664725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.424664725, -2.924664725}

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