2x^2-15x+10=0

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Solution for 2x^2-15x+10=0 equation: 


Simplifying
2x2 + -15x + 10 = 0

Reorder the terms:
10 + -15x + 2x2 = 0

Solving
10 + -15x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
5 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -7.5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -7.5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7.5x + x2 = 0 + -5
-7.5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-7.5x + x2 = -5

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -5 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -5 + 14.0625

Combine like terms: -5 + 14.0625 = 9.0625
14.0625 + -7.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.010398645 and -3.010398645.


Subproblem 1
x + -3.75 = 3.010398645

Simplifying
x + -3.75 = 3.010398645

Reorder the terms:
-3.75 + x = 3.010398645

Solving
-3.75 + x = 3.010398645

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 3.010398645 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.010398645 + 3.75
x = 3.010398645 + 3.75

Combine like terms: 3.010398645 + 3.75 = 6.760398645
x = 6.760398645

Simplifying
x = 6.760398645


Subproblem 2
x + -3.75 = -3.010398645

Simplifying
x + -3.75 = -3.010398645

Reorder the terms:
-3.75 + x = -3.010398645

Solving
-3.75 + x = -3.010398645

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -3.010398645 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.010398645 + 3.75
x = -3.010398645 + 3.75

Combine like terms: -3.010398645 + 3.75 = 0.739601355
x = 0.739601355

Simplifying
x = 0.739601355


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.760398645, 0.739601355}

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