4x^2-17x+10=0

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Solution for 4x^2-17x+10=0 equation: 


Simplifying
4x2 + -17x + 10 = 0

Reorder the terms:
10 + -17x + 4x2 = 0

Solving
10 + -17x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
2.5 + -4.25x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -4.25x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -4.25x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -4.25x + x2 = 0 + -2.5
-4.25x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-4.25x + x2 = -2.5

The x term is -4.25x.  Take half its coefficient (-2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
-4.25x + 4.515625 + x2 = -2.5 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = -2.5 + 4.515625

Combine like terms: -2.5 + 4.515625 = 2.015625
4.515625 + -4.25x + x2 = 2.015625

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(x + -2.125) equal to 1.419727086 and -1.419727086.


Subproblem 1
x + -2.125 = 1.419727086

Simplifying
x + -2.125 = 1.419727086

Reorder the terms:
-2.125 + x = 1.419727086

Solving
-2.125 + x = 1.419727086

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = 1.419727086 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = 1.419727086 + 2.125
x = 1.419727086 + 2.125

Combine like terms: 1.419727086 + 2.125 = 3.544727086
x = 3.544727086

Simplifying
x = 3.544727086


Subproblem 2
x + -2.125 = -1.419727086

Simplifying
x + -2.125 = -1.419727086

Reorder the terms:
-2.125 + x = -1.419727086

Solving
-2.125 + x = -1.419727086

Solving for variable 'x'.

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

Add '2.125' to each side of the equation.
-2.125 + 2.125 + x = -1.419727086 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = -1.419727086 + 2.125
x = -1.419727086 + 2.125

Combine like terms: -1.419727086 + 2.125 = 0.705272914
x = 0.705272914

Simplifying
x = 0.705272914


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.544727086, 0.705272914}

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