9x^2-30x-25=48

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Solution for 9x^2-30x-25=48 equation: 


Simplifying
9x2 + -30x + -25 = 48

Reorder the terms:
-25 + -30x + 9x2 = 48

Solving
-25 + -30x + 9x2 = 48

Solving for variable 'x'.

Reorder the terms:
-25 + -48 + -30x + 9x2 = 48 + -48

Combine like terms: -25 + -48 = -73
-73 + -30x + 9x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-73 + -30x + 9x2 = 0

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

Divide each side by '9'.
-8.111111111 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '8.111111111' to each side of the equation.
-8.111111111 + -3.333333333x + 8.111111111 + x2 = 0 + 8.111111111

Reorder the terms:
-8.111111111 + 8.111111111 + -3.333333333x + x2 = 0 + 8.111111111

Combine like terms: -8.111111111 + 8.111111111 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + 8.111111111
-3.333333333x + x2 = 0 + 8.111111111

Combine like terms: 0 + 8.111111111 = 8.111111111
-3.333333333x + x2 = 8.111111111

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 8.111111111 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 8.111111111 + 2.777777779

Combine like terms: 8.111111111 + 2.777777779 = 10.88888889
2.777777779 + -3.333333333x + x2 = 10.88888889

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 10.88888889

Calculate the square root of the right side: 3.299831646

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 3.299831646 and -3.299831646.


Subproblem 1
x + -1.666666667 = 3.299831646

Simplifying
x + -1.666666667 = 3.299831646

Reorder the terms:
-1.666666667 + x = 3.299831646

Solving
-1.666666667 + x = 3.299831646

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 3.299831646 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 3.299831646 + 1.666666667
x = 3.299831646 + 1.666666667

Combine like terms: 3.299831646 + 1.666666667 = 4.966498313
x = 4.966498313

Simplifying
x = 4.966498313


Subproblem 2
x + -1.666666667 = -3.299831646

Simplifying
x + -1.666666667 = -3.299831646

Reorder the terms:
-1.666666667 + x = -3.299831646

Solving
-1.666666667 + x = -3.299831646

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -3.299831646 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -3.299831646 + 1.666666667
x = -3.299831646 + 1.666666667

Combine like terms: -3.299831646 + 1.666666667 = -1.633164979
x = -1.633164979

Simplifying
x = -1.633164979


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.966498313, -1.633164979}

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