(10x^2)-25-3x=0

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Solution for (10x^2)-25-3x=0 equation: 


Simplifying
(10x2) + -25 + -3x = 0

Reorder the terms:
-25 + -3x + (10x2) = 0

Solving
-25 + -3x + (10x2) = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-2.5 + -0.3x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.3x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.3x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.3x + x2 = 0 + 2.5
-0.3x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.3x + x2 = 2.5

The x term is -0.3x.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3x + 0.0225 + x2 = 2.5 + 0.0225

Reorder the terms:
0.0225 + -0.3x + x2 = 2.5 + 0.0225

Combine like terms: 2.5 + 0.0225 = 2.5225
0.0225 + -0.3x + x2 = 2.5225

Factor a perfect square on the left side:
((x) + -0.15)((x) + -0.15) = 2.5225

Calculate the square root of the right side: 1.588238017

Break this problem into two subproblems by setting 
((x) + -0.15) equal to 1.588238017 and -1.588238017.


Subproblem 1
(x) + -0.15 = 1.588238017

Simplifying
(x) + -0.15 = 1.588238017
x + -0.15 = 1.588238017

Reorder the terms:
-0.15 + x = 1.588238017

Solving
-0.15 + x = 1.588238017

Solving for variable 'x'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + x = 1.588238017 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + x = 1.588238017 + 0.15
x = 1.588238017 + 0.15

Combine like terms: 1.588238017 + 0.15 = 1.738238017
x = 1.738238017

Simplifying
x = 1.738238017


Subproblem 2
(x) + -0.15 = -1.588238017

Simplifying
(x) + -0.15 = -1.588238017
x + -0.15 = -1.588238017

Reorder the terms:
-0.15 + x = -1.588238017

Solving
-0.15 + x = -1.588238017

Solving for variable 'x'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + x = -1.588238017 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + x = -1.588238017 + 0.15
x = -1.588238017 + 0.15

Combine like terms: -1.588238017 + 0.15 = -1.438238017
x = -1.438238017

Simplifying
x = -1.438238017


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.738238017, -1.438238017}

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