9x^2-42x+25=0

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Solution for 9x^2-42x+25=0 equation: 


Simplifying
9x2 + -42x + 25 = 0

Reorder the terms:
25 + -42x + 9x2 = 0

Solving
25 + -42x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
2.777777778 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.777777778' to each side of the equation.
2.777777778 + -4.666666667x + -2.777777778 + x2 = 0 + -2.777777778

Reorder the terms:
2.777777778 + -2.777777778 + -4.666666667x + x2 = 0 + -2.777777778

Combine like terms: 2.777777778 + -2.777777778 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + -2.777777778
-4.666666667x + x2 = 0 + -2.777777778

Combine like terms: 0 + -2.777777778 = -2.777777778
-4.666666667x + x2 = -2.777777778

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = -2.777777778 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = -2.777777778 + 5.444444448

Combine like terms: -2.777777778 + 5.444444448 = 2.66666667
5.444444448 + -4.666666667x + x2 = 2.66666667

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 2.66666667

Calculate the square root of the right side: 1.632993163

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 1.632993163 and -1.632993163.


Subproblem 1
x + -2.333333334 = 1.632993163

Simplifying
x + -2.333333334 = 1.632993163

Reorder the terms:
-2.333333334 + x = 1.632993163

Solving
-2.333333334 + x = 1.632993163

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 1.632993163 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 1.632993163 + 2.333333334
x = 1.632993163 + 2.333333334

Combine like terms: 1.632993163 + 2.333333334 = 3.966326497
x = 3.966326497

Simplifying
x = 3.966326497


Subproblem 2
x + -2.333333334 = -1.632993163

Simplifying
x + -2.333333334 = -1.632993163

Reorder the terms:
-2.333333334 + x = -1.632993163

Solving
-2.333333334 + x = -1.632993163

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -1.632993163 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -1.632993163 + 2.333333334
x = -1.632993163 + 2.333333334

Combine like terms: -1.632993163 + 2.333333334 = 0.700340171
x = 0.700340171

Simplifying
x = 0.700340171


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.966326497, 0.700340171}

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