4x^2-23x+10=0

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Solution for 4x^2-23x+10=0 equation: 


Simplifying
4x2 + -23x + 10 = 0

Reorder the terms:
10 + -23x + 4x2 = 0

Solving
10 + -23x + 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 + -5.75x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -5.75x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -5.75x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -5.75x + x2 = 0 + -2.5
-5.75x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-5.75x + x2 = -2.5

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = -2.5 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = -2.5 + 8.265625

Combine like terms: -2.5 + 8.265625 = 5.765625
8.265625 + -5.75x + x2 = 5.765625

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(x + -2.875) equal to 2.401171589 and -2.401171589.


Subproblem 1
x + -2.875 = 2.401171589

Simplifying
x + -2.875 = 2.401171589

Reorder the terms:
-2.875 + x = 2.401171589

Solving
-2.875 + x = 2.401171589

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = 2.401171589 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = 2.401171589 + 2.875
x = 2.401171589 + 2.875

Combine like terms: 2.401171589 + 2.875 = 5.276171589
x = 5.276171589

Simplifying
x = 5.276171589


Subproblem 2
x + -2.875 = -2.401171589

Simplifying
x + -2.875 = -2.401171589

Reorder the terms:
-2.875 + x = -2.401171589

Solving
-2.875 + x = -2.401171589

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = -2.401171589 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = -2.401171589 + 2.875
x = -2.401171589 + 2.875

Combine like terms: -2.401171589 + 2.875 = 0.473828411
x = 0.473828411

Simplifying
x = 0.473828411


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.276171589, 0.473828411}

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