3x^2+25x-7.5=0

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Solution for 3x^2+25x-7.5=0 equation: 


Simplifying
3x2 + 25x + -7.5 = 0

Reorder the terms:
-7.5 + 25x + 3x2 = 0

Solving
-7.5 + 25x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-2.5 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 8.333333333x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 8.333333333x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 8.333333333x + x2 = 0 + 2.5
8.333333333x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
8.333333333x + x2 = 2.5

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = 2.5 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = 2.5 + 17.36111111

Combine like terms: 2.5 + 17.36111111 = 19.86111111
17.36111111 + 8.333333333x + x2 = 19.86111111

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 19.86111111

Calculate the square root of the right side: 4.456580652

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 4.456580652 and -4.456580652.


Subproblem 1
x + 4.166666667 = 4.456580652

Simplifying
x + 4.166666667 = 4.456580652

Reorder the terms:
4.166666667 + x = 4.456580652

Solving
4.166666667 + x = 4.456580652

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = 4.456580652 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = 4.456580652 + -4.166666667
x = 4.456580652 + -4.166666667

Combine like terms: 4.456580652 + -4.166666667 = 0.289913985
x = 0.289913985

Simplifying
x = 0.289913985


Subproblem 2
x + 4.166666667 = -4.456580652

Simplifying
x + 4.166666667 = -4.456580652

Reorder the terms:
4.166666667 + x = -4.456580652

Solving
4.166666667 + x = -4.456580652

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = -4.456580652 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = -4.456580652 + -4.166666667
x = -4.456580652 + -4.166666667

Combine like terms: -4.456580652 + -4.166666667 = -8.623247319
x = -8.623247319

Simplifying
x = -8.623247319


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.289913985, -8.623247319}

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